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Fundamentals of Chemical Metallurgy

University of Miskolc

Faculty of Materials Science and Engineering

Tamás KÉKESI, DSc.

Professor

2018

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Contents 1 Introduction ............................................................................................................................................... 3 2 Raw Materials ............................................................................................................................................ 7

2.1 Genesis and types of natural raw materials ....................................................................................... 7

2.2 The relative amounts of raw materials and produced metals ......................................................... 19

3 Preparation of raw materials for metallurgical processing ..................................................................... 27 3.1 Mechanical liberation ....................................................................................................................... 28

3.2 Crushing ............................................................................................................................................ 31

3.3 Grinding ............................................................................................................................................ 33

3.4 Classification and separation of the ground particles ...................................................................... 36

3.4.1 Separation by physical properties ............................................................................................. 36

3.4.2 Separation by surface properties .............................................................................................. 44

3.5 Separation from the matrix phase ................................................................................................... 47

3.6 Agglomeration .................................................................................................................................. 49

3.6.1 Pelletizing .................................................................................................................................. 49

3.6.2 Sintering ..................................................................................................................................... 50

3.6.3 Briquetting ................................................................................................................................. 53

4 Metallurgical thermodynamics ................................................................................................................ 53 4.1 Gibbs free energy and activity .......................................................................................................... 54

4.2 Physico-chemical equilibria in chemical metallurgy ......................................................................... 58

4.3 The effect of temperature on the characteristics of the reaction ................................................... 61

4.4 Thermochemical examination of reactions ...................................................................................... 65

4.4.1 Determining the heat of reaction .............................................................................................. 66

4.4.2 Temperature dependence of the reaction heat ........................................................................ 69

4.4.3 The entropy change of the reaction .......................................................................................... 75

4.4.4 The free enthalpy change of the reaction and the equilibrium constant ................................. 78

4.4.5 Numerical examination of reaction feasibility .......................................................................... 80

4.5 The formation and reduction of metal oxides.................................................................................. 94

4.6 Dissolution and precipitation in aqueous media ............................................................................ 106

4.7 Electrode potentials and redox equilibria ...................................................................................... 111

5 The kinetics of metallurgical reactions .................................................................................................. 128 5.1 Determination of the rate constant ............................................................................................... 129

5.2 The temperature dependence of the reaction rate ....................................................................... 137

5.3 Experimental examination of the reaction rate and activation energy ......................................... 142

Test questions ........................................................................................................................................... 149 References ................................................................................................................................................. 152

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1 Introduction

Extraction, purification and alloying of metals is an ancient craft, although mankind could

only apply native metals, like gold and copper which could also be found in the elemental form.

However, even in the ancient times, a few thousand years ago, man discovered the way of

extracting some metals from suitable ores by applying reducing conditions at high temperatures.

The principle experience has arisen possibly from the firing of glazed pottery. This was the

primitive technology where the critical conditions of high temperature and reducing atmosphere

were available for the extracting metals out of the metal oxide components. by proper development,

this incident gave rise to the ancient production of larger masses of copper and bronze.

Even more, history and the development of civilization was in relation with the

possibility of metal production at certain areas of the world. The global distribution of economic

and political potential is still principally influenced by the local anility of producing valuable

materials. The knowledge of metal extraction lived basically on traditions. In the middle ages the

growing production rate and further on the industrial revolution raised the level of metal extraction

to veritable large scale production. Nowadays, there are huge enterprises operating all over the

world applying various technologies for the extraction of the number of metals required by practical

applications. However, the multitude of technological solutions are based on a few physico-

chemical principles and laws.

Chemical metallurgy discusses the processes providing the grounds for the modern

procedures in this trade, which affected even the turns in history. It requires primarily the

application of chemical and physico-chemical laws and relationships.

Metals exhibit mechanical and chemical properties which can be significantly modified by

alloying or purification. Besides, they are indispensable industrial materials because of their

properties of electrical and heat conductivity. Chemical metallurgical methods allow their ultra-

high purification, whereby the properties corresponding to common states can be significantly

changed. Super pure metals thus obtained are raw materials of the electronic industry.

Application of metals represent a vast range, including structural materials through surface

layers to raw materials for special composite or metal-compound type systems. Besides practical

applications, their use as ornamental, jewel and valorising functions cannot be neglected either.

Metal use expresses also the level of national or social development. Steel consumption was the

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common measuring tool to indicate the level of industrial or economic development in the second

half of the 20th Century. In the 21st century it is aluminium that seems more or less to take over this

role. As data organised in Fig. 1 referring to the larger countries in different economic areas of the

world show, relatively strong correlation can be found between the GDP pro capita values and the

aluminium consumption in the country [1OECD Global Forum on Environment, Materials Case Study 2 –

Aluminium, Mechelen, Belgium 25-27 Oct. 2010].

Fig. 1 The correlation of GDP and aluminium consumption in different countries (based on 2006

statistics [1]).

Metals can be obtained from different resources. Methods of extraction depend naturally

on the characteristics of the raw material and the properties of the metal and the main components

accompanying it. Primary resources are the various ores, usually containing the metal as its oxide,

sulphide or other compound. Secondary resources include by-products of some industrial

operations and wastes generated by consumption. As primary resources and various industrial by-

products contain the metal in compound state, extraction requires chemical decomposition of the

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compound. It may also happen that the ore contains the valuable component in elemental state,

since the reactivity of noble metals is very low. However, in this case the metal can be so dispersed

that extraction may require chemical methods by converting the metal into some compound form

and separating it thereby. The metallic fraction predominates generally in the case of metal scrap

and it is often significant in more complex wastes. Scrap metals can be melted directly to be

converted into a workable form after refining. Nevertheless, oxidation and slag formation during

melting makes chemical processes important also in such cases. In the case of complex secondary

raw materials, the different states of the various metals contained makes the conversion into some

compound form indispensable, allowing the selective metal extraction. It is worth, however,

changing the physical state and concentration of the metal in both the primary and the secondary

raw materials by beneficiating methods. Thereby it is aimed to set the advantageous physical and

chemical conditions beneficial for metal extraction.

Significance of chemical metallurgy is further enhanced by the growing need for purer and

purer metals. Efficient removal of homogenous impurities (dissolved metals) can be carried out

usually by selective reactions or electrolysis, but metal refining by physical-chemical methods

based on phase equilibria are also important. For designing, developing, or understanding these

processes of metal extraction and refining, it is important to know the major characteristics and

conditions. They have to be determined by the relevant material characteristics and parameters.

Therefore, it is primarily important to clarify the principles and characteristics applied in

thermodynamics and reaction kinetics. The possibility and extent of transformations are

determined by the energy states of the reactants and products, which depends on the quality,

distribution and temperature of the materials involved. The rate of reactions is fundamentally

determined by the reaction mechanism and the temperature. Chemical metallurgy discusses these

characteristics and relationships referring to typical metal extracting and refining technologies,

with the aim of direct metallurgical applicability. After clarifying the conditions and characteristics

of processes, the methods of application should also be considered. The physico-chemical

conditions of the reactions are usually provided either by the high temperature or by the ionic state

achieved through hydration. This is what gave rise to processes of pyrometallurgy and

hydrometallurgy, respectively. The valuable metal can be obtained from its compounds or from

its ionic solutions by reduction. The by-product of the thermic processes applying various – but

mostly carbon based – reducing agents is the slag, which is separated from the extracted metal or

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from the intermediate products containing the metal in an increased concentration. At the same

time, the electrometallurgical processes have also developed, which reduce the metal ions from

its aqueous solutions or molten salts preliminarily obtained by acid and alkaline leaching of the

raw materials. Electro-winning is operated with inert anodes, where a secondary gaseous product

is also evolved. A further by-product in hydrometallurgy is the solid residue from the leaching step.

The value of the metal is basically determined by its purity. It is necessary to strive for

selectivity and to ensure the purest possible product during extraction. However, it is impossible to

match the purity requirements of all the applications while a high yield and acceptable economy is

also to be maintained. There can be a number of impurities in the raw material that are carried

along by the main component during extraction to a higher or lower ratio even by the most modern

extraction procedures designed with the greatest care. There may be however, some valuable

elements among them, whose separation in the form of by-products may produce additional value.

Therefore, the metal extracted in a raw state needs to be further purified – refined – by chemical

metallurgical methods. This can be carried out by melt refining procedures relying on the

differences in reactivity or physical states of the components in the raw metal. Impurity elements

need to be transferred in separate phase by selective reactions. Besides the pyrometallurgical melt

refining technologies capable of removing larger amounts of some impurities, usually in multiple

steps, an option for removing the majority of remaining impurities in a single step can be the

electrolytic refining. The various elements behave in different ways during the electrolytic

dissolution of the anodes made of the raw metal and during the reduction of the ions at the cathode.

The purity of the cathode metal – expressed in percentage - is usually orders of magnitude higher

than that of the raw metal.

The methods outlined above are based on chemical reactions described relatively easily.

However, the execution and optimization of the processes requires a careful selection of the

conditions. All that can be based on chemical metallurgical knowledge and concept. This can be

applied for the utilization of primary raw materials and collected wastes to produce value from.

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2 Raw Materials

Metal extraction is based on rocks from certain locations of the Earth’s crust where the

aimed metal is contained at higher than average concentration and in a form suitable for processing.

Such mined primary raw materials advantageously suitable for metal extraction are referred to

as ores. The metal can be found mostly in oxide or sulphide compounds, but it can also occur in

the form of different salts (chlorides, sulphates, silicates, etc.). The type and amount of gangue

components attached to the minerals of the main element are also of importance. Processing of the

ores can be devised by considering all these characteristics.

In the cases of some metals, equal importance is represented by the secondary raw

materials – the metal scraps or the metalliferous (metal containing) waste materials. The energy

and the costs required for metal extraction is related to the steps of mining, ore beneficiation,

concentration, metal extraction and refining. In the case of metal scrap, the costs and the required

energy are limited to the collection, selection, preparation and the direct melting and melt

processing steps. However, the demands cannot be satisfied solely by the supplies of metal scrap.

The significance of ores remains great and the primary resources are available, but the efficiency

and sustainability of the applied technologies must be considered in developing technologies based

on chemical metallurgy.

2.1 Genesis and types of natural raw materials

Metals occur in various mineralogical forms and with very different abundance in nature.

metals are contained mostly in Earth’s crust, but there are extractable elements also in sea water.

Table 1 gives the bulk concentrations of the elements in the crust, according to current knowledge

[2David R. Lide (ed.), CRC Handbook of Chemistry and Physics, 85th Edition. CRC Press. Boca Raton, Florida

(2005). Section 14, Geophysics, Astronomy, and Acoustics; Abundance of Elements in the Earth's Crust and in the

Sea.]. The most important metals used in practice are highlighted in red colour and other metals

applied in industry are also marked by colour (in green). Non-metallic elements are given in grey

characters.

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Table 1 Abundance of elements in the Earth’s crust [2]

It may be surprising that a number of rare earth elements are more abundant than for example tin

and lead, nevertheless they are known as common metals by their general applications and ordinary

prices. The reason for that is the also very versatile tendency of geochemical concentration,

which is in favour of these elements. Due to specific geological conditions, ores can be found in

an uneven distribution in the Earth’s crust. Less abundant metals occurring in low average

concentrations may sometimes form deposits containing ores of high metal concentration. Ore

deposits in the lithosphere may be formed by internal magmatic processes ore external ones at the

surface, or by the combination of both.

The sulphide and the oxide melts tend to separate from each other, which is important not only in

the formation of ores, but also in the metallurgical processing. Further, the different minerals may

crystallize from the magma separately under different conditions (Bushweld-South-Africa,

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Zimbabwe, Sudbury-Canada). On the other hand, as a result of geological processes, the primary

ore deposits may occur in a transformed metamorphic state (Iron Spring – USA, Banat –

Romania). A large part of base metal ores has formed underground veins by hydrothermal

processes when the metal compounds precipitated from the aqueous solutions of high temperature

and pressure, or they may have formed segregations in sediment deposits after leaking to the

surface (Rammelsberg – Germany). Among the processes at the surface, the residual concentration

has a great role, whereby the soluble components are removed and the insoluble ones are

concentrated. This has given rise to the formation of bauxites and to the formation of lateritic nickel

deposits (New Caledonia, Jamaica and France). A further process at the surface is the

sedimentation, which results in the concentration of dense and refractory minerals (cassiterite

deposits – Malaysia, noble metal deposits – South Africa). Further on, metals leached from the

upper zones of the deposits may stream downwards and after precipitation, secondary deposits are

formed. Table 2 illustrates the limits of workability and the typical fac tors of concentration for the

different ores of various metals.

Table 2 Abundance, world production and typical criteria of workability data for some common

and less common metals in ores

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According to their physico-chemical properties, the elements are distributed in different ways in

the structure of the Earth. A conventional grouping is the Goldshmidt-system [3V. M. Goldschmidt:

The principles of distribution of chemical elements in minerals and rocks. J. Chem. Soc., 1937, 655-673.]. Metals

can be characterised basically as lithophylic, siderophylic, or chalcophylic types. The location of

these groups in the periodic system of elements is shown in Fig. 2.

Fig. 2 The Goldschmidt-system of the elements.[3]

The most numerous group is that of the – rock forming – lithophylic elements (Al, At, B,

Ba, Be, Br, Ca, Cl, Cr, Cs, F, I, Hf, K, Li, Mg, Na, Nb, O, P, Rb, Sc, Si, Sr, Ta, Tc, Th, Ti, U, V,

Y, Zr, W and the Lanthanides). Many of these are of low density and of high reactivity, forming

strongly bound oxides. They are unwilling to mix with iron, therefore they are not sinking towards

the deep core and can be found near the surface. These elements readily form ions – easily reacting

with oxygen – by giving away electrons from their s, f and d shells. Silicon, phosphorous and boron

- also belonging here form covalent bonds reinforced by – π-bonds – with oxygen, whereas the

alkali and alkaline earth elements form ionic salts with the halogens. The oxides of these elements

readily form silicates, which – due to their low densities - are stabilized in layers close to the

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surface. Among them, the more water soluble ones (alkali and alkaline earth elements) may have

been transformed by secondary concentration or got delivered into the sea water. The extraction of

lithophylic elements requires much energy and they can be detached from oxygen only by the

method of cathodic reduction. Thus their production could develop only in the modern era after the

evolution of the industrial use of electric current.

The siderophylic elements (Au, Co, Fe, Ir, Mn, Mo, Ni, Os, Pd, Pt, Re, Rh and Ru) can be

found in the central group of the transition metals. They are characterized by high densities and

high solubility in iron. Most of them have low affinities to oxygen, and even there are some

elements among them (e.g. Au) whose oxides are unstable thermodynamically. Bond to iron, they

are located towards the core of the Earth. There are some elements in this group, however, which

may form strong bonds with oxygen (Mn, Fe and Mo) which may form strong bonds with oxygen,

but in the absence of oxygen during the birth of Earth they concentrated to a great degree in the

deeper layers. Naturally, they can be found in the oxide state near the surface.

The chalcophylic elements are also found near the surface, as they formed stable and

undissolved compounds mainly with sulphur and non-metals other than oxygen that were unwilling

to sink towards the core. As these sulphides are denser than the oxides and silicates of the

lithophylic elements, they occur deeper in the crust. There some less metallic elements among them

(Se, Te) which formed volatile hydrides during the initial ages of Earth when oxidation-reduction

of hydrogen was the dominant process, thus they could stay in the terrestrial environment only at

a strongly reduced amount. There are some metallic elements in this group (Zn, Ga) which –

because of their relatively high affinity to oxygen – can be found in oxide state near the surface,

similarly to the lithophylic elements.

The Goldsmidt-type groups may overlap in certain cases. This is illustrated by Fig. 3, also

showing their locations schematically [4Márton I.: Ércteleptan-II, http://www.foldtan.ro/files/

BBTE_Ercteleptan_ eloadas2.pdf, 2011.].

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Fig. 3 The Goldschmidt-type terrestrial distribution groups of the elements.[4]

Although they do not represent a case of metallurgical potential, the atmophylic elements

should also be mentioned. They occur as gases or volatile liquids under the conditions characteristic

of the Earth’s surface. There are the noble gases among them, which have largely been lost from

the environment during the formation of the atmosphere.

Although the concentration of the calcophylic elements is low in the crust, they form the

most important non-ferrous ores. One reason for this is their relatively low affinity for oxygen, and

the other is the potential in utilising the energy content in the sulphide, allowing relatively low

energy requirement for their extraction. A further reason is the high – often of several orders of

magnitude - tendency of concentration. Rocks containing such calcophylic elements have emerged

close to the surface around many mountain sites of the Earth formed by tectonic plate movement.

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Besides the solid raw materials, natural waters may also carry extractable metal content.

The salt content of sea water (3.5 % on the average) may also mean a metallurgical resource,

although just a few of the occurring metals have notable concentrations. The salt content gets into

the ocean either directly by dissolution from the sea bed or indirectly, after being collected by the

rivers. The main components of sea water are given in Table 3 as average values [5Hirose, K.:

Chemical Speciation of Trace Metals in Seawater: Review, Anal. Sci., 22 (2006) 1055-1063]. The local values are

especially lower around the North Pole, and they are higher in the Mediterranean and tropical

environment.

Table 3 Average composition of sea water [5]

Concentration, %

O H Cl Na Mg S Ca K

85,84 10,82 1,94 1,08 0,1292 0,091 0,04 0,04

The concentrations of other valuable metals are just a few micrograms in a litre, therefore

the extraction of only the magnesium have advanced to a technological level, and also that only in

the most favourable locations. As opposed to the relatively diluted sea water, however, the higher

salt concentrations in special springs or lakes may offer better opportunities for processing.

Nevertheless, the natural resources of metal extraction are primarily the mined ores. The value of

the raw material is basically determined by the concentration of the targeted metal. The main

mineral components of the most important ores of the technologically most relevant metals are

given in Table 4. These can be primarily metal oxides, oxide salts or sulphides. Chlorides can also

occur, although they are exceptional in the cases of base metal ores.

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Table 4 The main characteristics of the major ores

Ore Main mineral

Type Metal conc.,% Name Formula Metal conc., %

Al 25 ~ 30

Boehmite,

Diaspore

AlO(OH), ill. Al2O3.H2O 45

Gibbsite Al(OH)3, ill. Al2O3.3H2O 35

Fe 50 ~ 70 Hematite Fe2O3 69

Magnetite Fe3O4 72

Pb 20 Galenite PbS 87

Sb 20 Antimonite Sb2S3 71

Mn 50 ~ 55 Pyrolusite MnO2 63

Manganite Mn2O3.H2O 62

Cr 40 ~ 45 Chromite FeO.Cr2O3 46

Ti 30 ~ 35 Rutile TiO2 60

Ilmenite FeO.TiO2 31

Mg

25 Magnesite MgCO3 29

12 Dolomite (Mg,Ca)CO3 13

5 ~ 10 Bischofite MgCl2.6H2O 12

Carnallite KMgCl3.6H2O 9

Bi 15 Bismutite Bi2S3 81

Zn 10 Sphalerite ZnS 67

Willemite 2ZnO.SiO2.H2O 54

Ni 5 Pentlandite (Fe,Ni)9S8 33

Garnierite (Mg,Ni)3.Si2O7.2H2O 25

Cu 1 ~ 4

Chalcopyrite CuFeS2 34

Chalcocite Cu2S 78

Malachite CuCO3.Cu(OH)2 57

Li 1 Spodumen LiAlSi2O6 4

Sn 3 Cassiterite SnO2 78

W 2 Scheelite CaWO4 64

Mo 1 Molybdenite MoS2 60

Hg 1 Cinnabarite HgS 86

Ag 0,01 ~ 0,1 Argentite Ag2S 87

Au 0,0005 ~ 0,01 Gold Au 100

Metals occur as mineral compounds in the ores. Ore deposits differ according to the type

of occurrence, the extent, mass and distribution of the valuable minerals. The economy of

processing a given ore body is determined by the depth, extent and dispersion of the location, and

is also influenced by the general geological topography and the distribution of the underground

water. If the ore is suitable for the extraction of more than one metal, it can be considered as

complex, and can be processed by special metallurgical techniques to produce more than one

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products. A certain metal can be contained in very different minerals, whose value may be

determined by the stoichiometric metal concentration and the chemical breakability of the

compound. The valuable compounds of ores are accompanied by gangue minerals. Their types and

relative amounts also influence the feasibility of metallurgical processing and the value of the

deposit.

Comparing the data in Tables 1 and 4 shows that the mined ores derive from specific

locations of the Earth’s crust where the given metal is significantly concentrated. However, the

stoichiometric metal concentration of the valuable minerals are never reached in the ores, as they

also contain larger amounts of gangue rocks. The latter are basically composed of silicate rocks,

consisting approximately 90% of the crust. Fortunately, however, not only their chemical, but also

their physical properties differ from those of the valuable mineral components. Therefore, they can

be separated to a certain degree still at the mining site by physical methods before the chemical

metallurgical processing. Usually, the economic extraction of the metal is only possible if a large

portion of the accompanying gangue minerals are removed by preliminary physical methods. The

concentrate, prepared in this way, can be the feed for chemical metallurgical processing, and the

gangue residue is disposed of, often re-cultivated later on. This preparatory step of mineral

processing is necessary especially before a pyrometallurgical extraction of the metal. Although the

large amount of gangue material could be separated as slag from the obtained metal melt, but it

would mean a great loss of energy and a poor utilization of furnace capacity. Before

hydrometallurgical processing, beneficiation of the ore may be required if the properties of the

raw material have to be changed by a thermal treatment for the extractability of the metal, or the

large quantity of gangue would interfere with the process. The chemical metallurgical extraction

implies the decomposition of the metal containing compound and the separation of the reaction

products in different phases.

The technically available primary resources of the Earth are limited. If the rate of mining

is further growing progressively, a shortage of the primary raw materials may arise in a few

decades. This tendency may result in a significant depletion of the resources within 60 – 70 years

even in the case of the most abundant iron ores [6Lester R. Brown, Plan B 2.0 Rescuing a Planet Under Stress,

W.W. Norton & Co., New York, 2006.]. However, the growth of production and consumption brings

about an increased rate of metallic and metal containing waste generation. Secondary resources

are more and more important raw materials for metal extraction. The majority of the primary raw

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materials can be found at the economically and technologically less developed territories, entailing

large costs of transportation to the technological centres, where much of the waste materials are

also produced. Direct utilization of the large amounts of waste generated in societies of developed

industry, economy and civilization is important both for the reasons of economy and environment

protection. It is technologically advantageous that the concentration of the valuable metal is

relatively high and often found mostly in the metallic or in a simple compound state in secondary

raw materials. Their processing – beyond the necessary physical separation and preparation -

requires identical or principally identical metallurgical technologies to those used for primary

raw materials. Therefore, it often happens that metallurgical plants, formerly receiving large

quantities of ores, are gradually converted for processing mostly secondary raw materials, thus

serving sustainability and environment protection. Primary processing capacities are gradually

concentrated close to natural raw material resources, where not only transportation but also the

costs and conditions of operation offer better economic potentials. It is not surprising that metal

extraction and waste processing are linked mostly in the cases of developed countries of

advanced industrial production and consumption. Trends of development are dictated not only by

the necessity but also the economic advantages of metal extraction from waste materials. The latter

aspect may be indicated by the following major characteristics:

significantly lower energy requirement,

simpler technology and less work power needed,

equivalent quality to metals obtained from primary sources,

lower amount of residues,

better fulfilment of environmental requirements.

These advantages are especially pronounced in the cases of deep mineral resources and metals

occurring in strongly bound compounds. Such an example is aluminium, whose production requires

less than 10 % of the energy consumed in primary production. This gives enough incentive that has

resulted in a higher ratio of scrap than 30 % in the metal production [7 http://www.epa.gov /osw/conserve/

materials/alum.htm #facts]. On the other hand, the extremely high amount of electric energy required

for the extraction of aluminium is provided by hydro- and nuclear power stations, with capacities

designed and reserved for this purpose. The ratio of scrap used for the production of lead is still

higher. The majority of lead is produced from scrap, which is based on the higher than 99% ratio

of collected spent lead acid batteries [8Arnout, S., Nagels, E., Blanpain, B.: Thermodynamics of Lead

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Recycling, Proc. EMC2011, European Metallurgical Conference, Düsseldorf, 26-29 June, 2011, 363-372]. The use

of scrap is also significant in the production of steel and copper, but there are such metals (like zinc

and nickel) which are mainly applied as coatings or alloying constituents, thus they do not

contribute much to the supply of secondary raw materials for the production of the respective

metals.

Recycling scrap from consumption may also cause economic or technological

difficulties, such as:

the price of scrap is strongly influenced by market conditions,

it is difficult to determine the average composition of scrap is,

it is difficult to plan the availability of scrap supply,

the efficiency of collection is changeable,

it is a keen task to sort and prepare the scrap,

impurities that are hard to remove can get into the produced metal,

it is difficult to control the composition of the obtained melt.

A special and highly advantageous case is the use of technological scrap, whose purity

and composition can be guaranteed. The quantities of the contained elements brought into the

system by them can be accounted for in composing the charges to be melted. The added materials

can be calculated according to the targeted composition and the specific losses. The work of the

furnace man is aided by production systems applying computer software based on chemical

metallurgical conditions, which take the compositions of the produced alloy and the charged

materials, as well as the programmed technological parameters into consideration. As there are

such elements whose removal from the base metal is inefficient or impossible by the usual methods

of refining, some metal extracted from primary resources will be always required to avoid

excessive accumulation of such impurities.

Collection and preparation of scrap before metallurgical processing is carried out by a

number of smaller or larger enterprises. The major techniques of scrap preparation are sorting, the

possible removal of undesired materials – thereby the concentration of the valuable metal – and the

formation of the suitable shape, also assisting transportation. Metal scrap thus represents significant

commercial value and their transportation is not restricted by special regulations referring to

hazardous waste. Their use is therefore limited only by their available supply. Authorities are

striving to eliminate the irregular ways of their collection by strict procedures of trading ad

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registration. The value of metal scrap can be illustrated by the purchase prices expressed in

relation to the London Metal Exchange (LME) prices of the raw metal ingots. The average prices

– disclosed over the internet – of English, Canadian and Hungarian scrap dealers for high quality

metal scrap relative to the LME prices and the prices of the metal relative to that of common steel

are given in Table 5.

Table 5 The prices of commodity metals at the London Metal Exchange relative to that of

common steel and the relative prices of their scrap

Relative price Metal

Steel Al Cu Zn Pb Sn Ni

metal / steel 1 13,04 51,15 13,57 15,26 143 102

scrap / stock ingot 0.64 0,62 0,80 0,58 0,51

The scrap prices are not indicated for tin and nickel. In the former case, only the soldering waste

produced by the electronic industry could be figured, which is almost metallic, but the total amount

is usually covered by exclusive contracts by certain scrap dealers. In the latter case, the way of

applications does not allow significant amounts of scrap to be recycled.

Naturally, metallic scrap is and should be used for the production of metals with advantage.

However, there are other types of solid or liquid waste materials arising from the operation of

various industries as by-products, which contain metals in compounds. Among them, there are

large quantities of flue dusts, drosses from melting, solidified or crushed slags, sludges from

aqueous technologies and industrial waste liquors. A multitude of such – mostly hazardous waste

- materials can be found in the European system of waste materials associated with certain EWC

codes [9http://www.nwcpo.ie/forms/EWC_code_book.pdf]. The processing of such materials does not only

imply alternative resources of raw materials, but also means active environment protection. Besides

the value of the recovered metal, saving the very high costs of storing hazardous wastes is also a

significant economic gain. The recovery of valuable metals from such metal compounds require

the properly modified versions of the procedures applied for the primary raw materials.

In addition to or in connection with the extraction and refining of metals, chemical

metallurgy offers efficient methods for waste treatment and environment protection, indispensable

in modern societies.

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2.2 The relative amounts of raw materials and produced metals

While the utilisation of secondary raw materials has been increasing during recent years, the

growing need for metals does not allow any relapse either in the application of ores. The growth of

industrial production has served as the basis for a rising trend in metal recovery especially since

the middle of the 20th Century. This is illustrated by Fig. 4 constructed from the production data of

the most important structural metals [10Krone, K.: Aluminiumrecycling, Ver. Deutscher Schmelzhütten,

Düsseldorf, 2000].

Fig. 4. The production of the most important metals during modern times.

A progressive tendency of several decades indicate the effects of World War II and the subsequent

intensive infrastructural development. At the end of the 20th Century however the trend changed

for a more constant development, according to the growth of the global economy. Except for some

uncertainties caused by the economic crisis around 2008, this tendency has continued in the 21st

Century too. In the meantime, traffic and transportation achieved a revolution and due to its special

properties, the production of aluminium has become the second to that of steel, although for the

20

total value, copper has maintained its position. These two non-ferrous metals can be considered by

their properties as special and practically irreplaceable.

Comparing the amounts of mined ores of known extractable metal contents to the amounts of the

produced metals may refer also to the significance of the raw material types. Figures 5-9 show the

tendencies for the most important technical metals as constructed from the production data

published by the British Geological Survey for the 1995 – 2011 period [11-15Stockwell,L.E., Hillier,J.A.,

Mills, A.J., et al.: British Geological Survey 2001, World Mineral Statistics, 1995-99: production: exports: imports.,

Stockwell,L.E., Hillier,J.A., Mills, A.J., et al.: British Geological Survey 2002, World Mineral Statistics, 1996-2000:

production: exports: imports. Minerals Programme Report No.10., Taylor,L.E., Brown,T.J., Benham,A.J. et al.: British

Geological Survey 2006, World Mineral Production, 2000-04., Brown,T.J., Hetherington,L.E., Hannis,S.D., et al.:

British Geological Survey 2009, World Mineral Production, 2003-07., Brown, T.J, Shaw, R.A., Bide, T. et al.: British

Geological Survey 2013, World Mineral Production, 2007-11].

Fig. 5 The production of iron ore, pig iron and steel between 1995 and 2011.

The mass ratio of pig iron to the iron ore referring to the period before 2005 indicates a steady

supply of the raw material and also the average iron concentration in it. The lower demand after

the 2008 global economic crisis resulted in an obviously decreased production rate of all the metals.

The ratio of the produced steel and pig iron shows the relatively stable rate of steel scrap used as

21

a raw material. A similar comparison can be made for the produced masses of bauxite and

alumina, shown in Fig. 6. A practically constant ratio of the latter two products can be seen in the

period up to approximately 2005, corresponding to the recovered aluminium oxide content of the

bauxite, in general. The economic crisis also hit the equilibrium in the production and processing

of bauxite. In the case of alumina and the primary aluminium obtained from it, proportionality

can be upset only by the changes in the stocks, as alumina is a practically pure Al2O3 compound

whose reduction yields the metal with the standard reduction technology of generally uniform

efficiency. Secondary aluminium obtained from scrap melting is not represented in the figure,

although it gives more than a third of the primary aluminium production [1OECD Global Forum on

Environment, Materials Case Study 2 – Aluminium, Mechelen, Belgium 25-27 Oct. 2010], and even more

aluminium is produced from scrap than from bauxite in Europe.

Fig. 6 The production of bauxite, alumina and primary aluminium between 1995 and 2011.

In the case of copper, Fig. 7 shows the metal content in the mined ore, the amount of the raw metal

produced from it and the total amount of the refined product. The latter also includes the share of

the metal produced from secondary resources.

22

Fig. 7 The amount of copper in the mined ores and that of the produced raw metal and the total

refined metal output between 1995 and 2011.

Figure 7 clearly demonstrates the relative use of the primary and the secondary raw materials.

The increasing difference between the top and the bottom curves corresponds to the growing rate

of the copper scrap use during the first decade of the 21st Century. This tendency is bound to

strengthen further as the collection and the treatment of scrap is becoming more and more efficient.

Two utterly different structures of raw materials are illustrated in Fig. 8 by the

respective data of the ore and metal outputs. In the case of zinc, the metal contained in the mined

ore exactly corresponds to the amount of the produced metal. The metal loss involved in the

chemical metallurgical processing may be practically equal to the amount of zinc obtained from

the secondary resources (scrap and oxide flue dust) of minor importance. In the completely

different case of lead, however, the amount of the finally produced pure metal is more than double

of the metal content of the mined ore. This indicates a high degree of scrap recycling.

23

Fig. 8 The amounts of zinc and lead in the mined ores and those of the produced pure metals

between 1995 and 2011.

Reflecting the case of zinc, a similar raw materials structure is suggested for nickel and tin by Fig.

9. The uses of these metals either do not produce much pure nickel or tin scrap, therefore the

production depends strongly on the availability ores and on the primary chemical metallurgical

technologies.

Fig. 9 The amounts of nickel and tin in the mined ores and those of the produced metals.

24

The comparison of the production records reveals, that in the cases of the most important metals

applied in industry, scraps are significant raw materials, but the use of ores are still essential. Ore

reserves cannot be endless but they are available still for several decades in the cases of all the

important metals. Ore exploration is also continued, and it is carried out by more and more modern

techniques. Beyond the knowledge of the processes of ore formation and the characteristic signs at

the surface, more versatile and accurate methods of geological investigations are at our disposal.

The disturbances caused by large ore bodies in the magnetic or gravitational fields can be detected

by highly sensitive instruments. Also, seismic signals and classical or radiological methods of

analysis can assist the efficient exploration. However, the detected ore body has to be located by

executing deep drilling at multiple points and the analysis of the core samples by layers. Mining

and designing of the economical extraction technology can be started only subsequently. The

method of processing is determined by the type of the occurrence of the metal in possible

compounds:

Virgin metal (this form is characteristic only of the noble metals, but copper can also

appear in this form);

Oxide minerals (characteristic occurrence of reactive metals also in the primary magmatic

rocks and it may be formed from deep sulphide occurrences of other metals by oxidation

close to the surface);

Halide minerals (characteristic occurrence of the most reactive metals – such as the alkali

and alkaline earth metals – of the most negative electrode potentials, which – because of

the high solubility – are present in sea water);

Oxide salt minerals (besides the sulphate rocks and carbonates of secondary origin, the

complex oxides, silicates, titanates and phosphates dispersed in the igneous granite rocks.

The latter can form ores practically only by secondary concentrating processes in

sediments.);

Sulphide minerals (resulting from deep hydrothermal processes of ore formation. They are

characterised by complex occurrences - – Pb-Zn-Ag, Zn-Cd, Cu-Fe, Ni-Fe, Ni-Co – and

iron is the usual accompanying metal.);

Arsenides occur in smaller quantities beside the sulphides in the cases of Cu, Ni and Co.

The pure sulphide forms are more characteristic and more valuable.

25

The secondary raw materials are basically metallic, but the industrial by-products often

contain the metals in oxide, hydroxide, oxide salt or halides. Chemical metallurgical methods can

be applied generally for all kinds of raw materials.

More than one valuable metals can be extracted from complex ores. The significance of an ore

deposit is given by the extractable main and accompanying metals and the possible by products.

This needs to be compared to the costs of exploration, mining, mineral processing, transportation,

gangue disposal, re-cultivation on the one hand and the metal extraction, refining and casting on

the other. Additionally, the overhead and marketing costs also have to be covered. Therefore, large

reserves are known, which – due to the current economic conditions – do not qualify as ore deposits,

but changing circumstances may make them worth considering. Besides the valuable minerals in

the ores, the gangue components may also be marketed in certain cases. For example, the sulphide

veins may be accompanied by marketable fluor-spar or barite minerals, or the usually abundant

iron sulphide, the pyrite. The latter components can be utilised as energy carrier materials or

additive reagents. The most important raw materials of sulphur or sulphuric acid production are the

metal sulphide minerals. At the same time, sulphuric acid production must be associated with metal

extraction from these materials so as to avoid sulphur dioxide emission. The value of the potential

by-products may depend on the presence of a local demand. However, a direct cost analysis may

not be enough. The price of the strategically important metals is traditionally rather unstable.

Beyond the production costs, a fundamental factor is the level of accumulated stocks. This is

illustrated by the time curves of nickel, lead and zinc prices in Fig. 10.

Fig. 10 The prices and stocks of Ni, Pb and Zn during the period of 1991-2007.

26

However, the standard prices of the London Metal Exchange (LME) do not reflect only the levels

of stocks but they also react to the political scenery with strong deviations. As the investment cost

of metal production are high, new facilities are installed only on the bases of assured raw material

supply and a growing demand supported by technological development. If that happens, a

significant social and infrastructural development is linked to it locally.

There is a correlation also between the price and the production output of a metal, which is

illustrated in Fig. 11 by the examples of steel and copper.

Fig. 11 The relationship between the prices and the production of steel (a) and copper (b)

during the period of 1991-2007.[11-15]

The market price of metals, influenced by the stocks and the political situation, also controls the

utilization of the production capacities. Some of which may be shut down temporarily during in

cases of low market prices for minimizing the operational expenses. The higher specific costs

arising from the idle period can be paid back at the following cycle of price rising prices. Therefore,

this practice is justifiable under the circumstances of undulating market conditions, but only the

production capacities with ample of capital, labour force and supply can afford it on a longer run.

Without these special conditions, the metal producing company may easily go bankrupt.

Besides the concentration and type of the main components, the value of the ore is

influenced by the types of the gangue minerals. An excellent property of metals is their separation

a) b)

27

in molten state from the compound materials. This gives the basis for pyrometallurgical

processing, where the reduced metal melt of high density finally separates itself physically from

the slag composed of molten oxides and accumulating above it. The quality of separation depends

on the composition of the slag, thus from the gangue components of the raw material. The proper

conditions are usually assured by fluxing additives composed of suitable oxides or by a suitable

mixture of different ores containing the gangue components in different proportions.

3 Preparation of raw materials for metallurgical processing

The extraction of metals from primary raw materials requires the decomposition of the compound

constituting the valuable mineral, i.e. the reduction of the metal. The noble metals are exceptional,

as they are in a reduced form in the raw material. In this case, however, difficulties arise from the

extremely low metal concentration found as microscopic particles dispersed in the carrier rock.

These difficulties may also be overcome by the application of chemical methods. Metal extraction

can be carried out directly at the source of the raw material or it can be transported for chemical

metallurgical processing after a suitable physical treatment resulting in a concentrate. As the metal

concentration in gold ores is usually very low, even after any ore preparation, extraction may take

place on or near the mining site. The latter process requires relatively little energy and chemical

consumption and the volume of the produced metal is low, therefore easily transported, but special

precautions are necessary because of the highly concentrated value involved. The large quantities

of bauxite or iron ore are generally transported because the gangue content is orders of magnitude

lower in these cases and the metal extraction implies much more energy. Thus the centres of metal

extraction may be located according to the availability of inexpensive energy – often supplied by

hydroelectric stations – and the good quality metallurgical coke – as the main reducing agent - and

the vicinity of the technologies further processing the large amounts of the produced metal.

Extraction of the metal is more economical if the raw material is more concentrated. Large

contents of the gangue may use significant melting capacities and may strongly increase the energy

consumption. Hydrometallurgical metal extraction may also require a preliminary concentration if

solubility is assured by a thermal preparation of the raw material. Physical concentrating treatment

of the raw material has to be carried out at the mining site, thus avoiding the transportation of the

28

rejected gangue material, whose disposal can be arranged easier at the mining areas lying far from

the industrial and municipal environment.

3.1 Mechanical liberation

Due to the large size and heterogeneous composition of its pieces, the mined or collected

raw material is not suitable for direct metal extraction. Primary raw materials brought up above the

surface are usually in the form of large and heterogeneous chunks and pieces. The crystals of the

valuable metal compounds and those of the accompanying minerals are embedded – more or less

dispersed - in the gangue rock matrix. Whatever was the way of ore formation, the presence of

gangue minerals is general. The precondition of separating the mineral grains of different

properties is the grinding of the raw material to a particle size commensurate with the grains to be

separated. This is referred to as mechanical liberation, which renders the phases of different

physical properties accessible usually in more or less separated particles.

The first step is the crushing, followed by the grinding of the raw material in different

mills to reach the required – usually finely powdered – particle size. Reaching fine particle sizes is

a long and multi-step process, while the operation of the mills consumes a great deal of energy.

The cost of grinding is strongly dependent on the distribution and the types of the mineral

components. Although it implies considerable costs, the efficiency of the subsequent separation

and concentration depends on the degree of mechanical “liberation”. The further costs of metal

extraction are, in turn, also influenced by the degree of concentration, whatever kind of chemical

metallurgical method will be chosen in accordance with the chemical composition of the material.

In the ideal case when the ore should crack along the borders of grains consisting of either

valuable or worthless components, grinding to the grain size would result in either valuable or

worthless particles. But the material is more or less coherent and the crack lines do not follow

exactly the grain boundaries. If – independently from the boundaries – they cross the grains

inside, the purity of the obtained particles will rely on the fineness of grinding. Figure 12 shows a

schematic cross section of an idealized piece of ore. In it, the valuable and the gangue grains are of

identical size, and the division of the crack lines is equal to the half of the linear grain size [16Gaudin,

A.M.. The Principles of Mineral Dressing, McGraw Book Co. 1939.].

29

Fig. 12 Cracking the ore of uniform cross section and regular shape consisting of coherently

bound valuable and gangue grains with planes divided by half the length of the grain size [16].

With this division, a quarter of the ground particles will be homogeneous and three quarters equally

mixed heterogeneous. One eighth of the particles will contain only valuable and another eighth

only gangue material. Thus, grinding can separate the components to a certain degree even if the

cracking system is completely independent of the grain boundaries. The ratio of the homogeneous

particles can be increased by decreasing the particle size of grinding. Due to the related costs, the

size reduction is usually limited, to four times that of the still recoverable smallest particle size

[17Gilchrist, J.D.: Extraction Metallurgy, 2nd Ed., Pergamon Press, Oxford, 1980.]. Most often it means a final

particle size of 100 µm. Depending on the properties of the material, the particle size spectra

obtained after multiple grinding steps are of different width. If a significant portion of the particles

are smaller than approximately 50 µm, a sludge fraction arises, which causes difficulties in further

processing, or causes considerable losses of the material.

The steps of the comminution procedure include the preliminary crushing (to ~ 5-10 mm

average size), coarse grinding and fine grinding. Due to the inherent macro cracks, the larger pieces

break easier. A less tangible, still obvious difference between crushing and grinding is in the effects

exerted on the pieces of the material.

During crushing, the large pieces fall apart along the main cracking lines, yielding smaller

pieces. Their shape is irregular, characterised by a great number of edges and tips. The internal

structural defects also result in smaller particles. The raw material - consisting originally of

approximately similar pieces by size – is split into two fractions of different average particle sizes,

30

referred to as coarse and fine portions. Their relative masses change with further comminution,

during which mainly the larger pieces suffer mechanical effect, therefore their size approaches the

largest ones in the powder fraction.

During grinding, practically all the particles may suffer approximately the same

mechanical effect causing the material to develop finally a unimodal although not symmetrical

granulometric distribution. Figure 13 shows the change of granulometry as the material of

originally relatively homogeneous size structure is ground in consecutive steps.

Fig. 13. The granulometric distribution in the material - consisting of coherent valuable and

gangue grains of equal diameter and regular shape - after consecutive steps of sectioning with

parallel planes at a distance of half of the grain size.

The effect of attrition enhances the generation of fine particles. It enhances the generation of small

particles by breaking off the surface roughness of the brittle material. The third mechanism is the

impact breakage, when the free particles are hit with great energy by grinding bodies or other

particles, and the kinetic energy causes internal stress, which results in comminution along the

internal surfaces determined by the structural heterogeneity of the particle. The machines working

on this principle are especially suitable for the liberation of valuable minerals entrapped in pieces

of heterogeneous ores.

31

3.2 Crushing

The rough crushing of the mined ores, consisting of large pieces, is carried out with jaw, cone,

circular or cylindrical crushers. In the former two cases, a moving jaw presses the pieces against

a fixed lateral surface of plane or conical shape, while the material is broken. The produced smaller

pieces are further broken as they travel towards the narrower space. The breaking surfaces are

always made of hard, high-manganese – Hadfield – steel. The movement of the jaws can be

modified so as they generate not only compressing forces but also some attrition. The most suitable

for this purpose is the circular or conical version. As a result of the forces causing complex motion,

fine abraded particles are generated in larger amounts, thereby increasing productivity and the

average size reduction. However, in the case of softer more ductile materials, the suitable method

applies simple compressing forces. The simple or compound pendulum jaw crushers shown in

Fig. 14 offer flexibility and allow large pieces in the feed [18Csőke B.: Fő méret- és üzemjellemzők

meghatározása az aprítóművek gépeinél, Építőanyag, 58, 4, 2006,107-112]. Equipment used in mines can

receive material containing even as large pieces as a few metres in diameter. Their capacity may

reach several hundreds of ton in an hour and the average size reduction can be 5 – 10 fold. The

crusher plate moves with a frequency of 1 – 6 Hz. It is however possible to reach finer particles –

although from smaller size feed - with the circular crushers, shown in Fig. 15a. In this case, the

pieces are broken by compression among them, which reduces the wear of the breaking surfaces

made of expensive material. Their capacity may significantly surpass that of the jaw crushers if

hard materials are treated. The structure of the cylindrical crushers – as shown in Fig. 15b – is

relatively simple, but they can receive the feed within a narrow size range and the average size

reduction is only about threefold. As there is very little interaction among the particles and the

superficial rubbing effect is weak, this method yields the lowest amount of fines and the wear of

the cylinders can be severe when hard material is crushed. Applying more cylindrical crushers in a

row with reduced gaps and setting relatively low degrees of size reduction – also removing the

undersize fraction by sieving – it is possible to obtain a granulometry of extremely narrow size

fractions. A further advantage of this technique is the ability to treat wet and sticking materials,

which tend to clog the jaw and conical crushers.

32

Fig. 14 The schematic of simple (a) and compound (b) pendulum jaw crushers (H – height of the

fixed jaw plate, G – feed port, R – discharge opening) [18].

Fig. 15 Structures of a typical circular crusher (a) and cylindrical crusher (b).[17,18]

During the preparation of ores, the largest pieces of rock coming from the mine are pre-

crushed in jaw crushers, then it can be further reduced usually to a size of 50 mm particle size in

(a)

(b)

(a)

(b)

33

Symons-type cone crushers (Fig. 16a), followed by the secondary crushing with conical,

cylindrical or impact crushers (Fig. 16b) to reach a particle size of about 5 mm or below.

Fig. 16 The structures of the conical (a) and the impact (b) crushers. [17-18]

The advantage of the conical crusher is the great output coupled with the relatively small

dimensions and the automatic cleaning of the discharge gap by the cyclic openings during rotation.

The impact crushers are usually applied for the comminution of weaker, brittle materials, but they

can be useful also for sticky, ductile ores because clogging rarely happens in this equipment.

However, excessive wear can be seen in the cases of too hard materials. The breaking effect in the

impact crusher is exerted by the hammer heads or by the collision with the other ore pieces and the

wall. The largest machines can handle as large pieces as 1 m in diameter and the throughput can

reach 2000 t/h with a reduction degree of approximately 40. The obtained particles are free of

mechanical stress. The latter property may be important when metallurgical slags are crushed

before the utilisation as construction materials.

3.3 Grinding

The particles obtained from crushing need to be ground to a finer state for a better mechanical

liberation. For this purpose, horizontal barrel shaped rotating mills, filled with grinding balls or

rods are generally used. Such a piece of equipment is schematically drown in Fig. 17. The inner

surface of the rotating drum is lined with a hard and replaceable lining. The pieces of the crushed

ore are hit by the grinding bodies (iron and steel balls, or rods) falling back from the rotating wall.

To increase efficiency, the lifting of the grinding balls or rods is assisted by ribbed wall surface.

34

The parts exposed to wear are traditionally made of manganese (13%) steel (Hadfield), but smaller

units may be lined with rubber for satisfactory performance and lower noise.

Fig. 17 The schematic structure of the ball mill. [17]

The feed is mixed with water to yield a humidity degree of approximately 25 – 50 %, and it travels

along the axis during rotation and is discharged through an opening at the opposite front covered

by a grille of the desired mesh grade. The primary role of the grille is to prevent the grinding balls

from leaving the mill, but it also retains the oversize particles. The balls are of different diameters,

which helps fine grinding but is a direct consequence of gradual wear and periodic replacement.

The efficiency of grinding is provided by the huge number of impacts.

The rotation speed needs to be set so as the balls should rise beyond the two thirds of the

internal height dropping back towards the coarser particles accumulating at the opposite side

diagonally. The grinding bodies stay clinging to the wall longer with higher rotation speed. In a

ball mill of D [cm] inner diameter, the critical rotation speed (nc in r.p.m.) – when the balls do

not fall and grinding stops – can be calculated as:

𝑛c = √𝑔2𝐷

100

60

𝜋≅

423

√𝐷 (1)

It is inversely proportional to the square root of the inner diameter. With a close to 50 % filling

degree and ribbed walls, the optimum conditions are reached at about 75% of the critical rotation

speed. However, a significant slip may occur between the charge and the smooth wall at low levels

35

of filling, when the critical rotation speed – resulting in “centrifuging” – may be significantly higher

than the theoretical value expressed by formula (1). In this case, the mill may be operated at higher

velocities than the theoretical maximum, yielding higher milling efficiency because of the stronger

effect of rubbing, but it also results in a stronger wear of the lining and the grinding bodies. This

also causes contamination of the material. If the material is to be protected against contamination

with iron, ceramic or rubber linings and hard quartz or flint grinding bodies are applied. The

diameter of such mills are smaller, what serves the protection of the grinding balls, but the lower

efficiency is compensated by a longer barrel in this case. As a further variation, it is possible to

replace the spherical grinding bodies with thick steel bars inserted parallel to the axis of the mill.

The advantage of the rod mills is the preferential grinding of the coarser particles, yielding a more

uniform garnulometric distribution in the product. The larger particles are stuck between the rods,

while the finer particles are driven by the stream of the aqueous phase among the rods towards the

discharge. Thus sludge formation can be avoided and the oxidising effect can be mitigated, if that

is required. Nevertheless, more attention has to be payed to the wear of the grinding rods and their

consequently happening incidental breakage.

The autogenous grinding is operated with air injection in mills of significantly greater

diameter relative to their length. The particles carried out by the air stream are divided into two

directions in a cyclone separator. The oversize particles are returned to the raw material for re-

grinding, thus producing the suitable particle size range. In this case, the larger pieces of the

material are used as grinding bodies. With larger diameters, also the pieces of the less dense ores

may fall with enough kinetic energy, but the suitably wide range of sizes should also be assured.

The brittle materials of heterogeneous grain structure are usually more suitable for this technology,

which is the least expensive option in this case.

The classification by the particle size and the recycling of the oversize particles are usual

steps not only in combination with the autogenous grinding, but it is also applied with the most

frequently used mills. In such a closed process scheme, faster material flow is coupled with lower

sludge formation and the granulometric distribution of the product is more controllable. In rod

mills, similarly to the jaw crushers, also the breaking process produces more regular particle size,

therefore, the open process scheme – omitting the partial recycling - is the characteristic way of

operation. The proper control of the particle size range in the product may be expensive, but it may

also strongly influence the efficiency of further processing.

36

3.4 Classification and separation of the ground particles

In view of further processing, it may be important to divide the ground materials into more

homogeneous size fractions. Because of the large quantities and the small sizes, it cannot be

executed manually. Keeping the ground material in movement, the different fractions have to be

directed in diverging direction according to the characteristic physical properties. The basic task is

the classification of the particles by size, by which the size range compatible with the processing

technology can be provided.

3.4.1 Separation by physical properties

By sieving, large amounts of the particles can be separated to fractions below and above

the given mesh size. The ground material can be divided further into different size fractions by

consecutive sieves of decreasing mesh sizes. The surface of a sieve is built up generally of

rectangular openings created by rods or wires placed perpendicularly to one another, although the

version formed of a plate with circular holes drilled in it is also possible. The mesh grade, often

used for the finer (less than a few millimetres) range, expresses the solid dividing lines - of

approximately equal width as the openings – along one-inch distance. The roughest sieve may be

of 4 mesh (with 4.75 mm openings) and the finest is of 500 mesh (with 0.025 mm openings).

Separating the particles of diameters close to that of the size of the openings requires moving,

during which the particles try to pass the hole from changing directions. For this reason, shaking

plane sieves or appropriately slanted rotary drum sieves can be used. It is essential in all cases to

maintain the optimum level of sieve filling, which is a few times the average particle size.

Furthermore, the openings need to be cleaned by some mechanical means.

Beyond the separation into particle size ranges, further methods of classification are

possible after fine grinding the originally very heterogeneous ore. An essential process is based on

the differences how the particles of different types move in a liquid or gas fluid under the effects

of gravity, buoyancy and drag forces. The sedimentation of the solid particles has a great

importance not only in classification but also – as to be seen later – in the hydro- or

pyrometallurgical extraction and the refining of metal melts. Therefore, it is worth examining the

fundamental principles in more detail. Among the forces contributing to the process of gravity

separation, the weight force of an ideally spherical particle of density and d diameter and the

37

buoyancy force originating from the medium of o density can be expressed simply. The drag

exerted on the particle by the medium always depends on the relative velocity, however the

relationship may be linear or quadratic. The medium around an ideally spherical and slow moving

particle shears open and produces a laminar flow. The resultant counteracting (Fe) drag force –

according to Stokes’ law is:

𝐹𝑒 = 𝐹𝑙𝑎𝑚 = 3𝜋𝜂𝑑𝑣 (2)

proportional to the particle diameter (d) the dynamic viscosity of the medium (, Pas) indicating

the shear resistance and the relative velocity (v). But with higher velocities, a turbulent flow is

formed around the particle, which implies also the moving of the continuous medium besides its

shearing. Thus – according to Newton’s law – the drag force becomes:

𝐹𝑒 = 𝐹𝑡𝑢𝑟𝑏 =𝜋

8𝜌𝑜𝑑

2𝑣2 (3)

proportional to the square of the diameter and the relative velocity of the spherical particle. The

resultant force determines the acceleration (a) of the particle according to the third law of dynamics:

1

6𝑑3𝜋(− 𝜌𝑜)𝑔 − 𝐹𝑒 =

1

6𝑑3𝜋𝜌𝑎 (4)

The acceleration of the particle under laminar or turbulent flow conditions can be expressed as

follows:

(𝑑𝑣

𝑑𝑡)𝑙𝑎𝑚

=−𝜌𝑜

𝑔 −

18𝑑−2𝜂𝑣

𝜌 (5)

(𝑑𝑣

𝑑𝑡)𝑡𝑢𝑟𝑏

=−𝜌𝑜

𝑔 −

3

4

𝜌𝑜

𝑑−1𝑣2 (6)

As the drag force from the medium is increasing with the velocity, the acceleration is quickly

terminated, and the maximum velocities (vmax):

38

(𝑣𝑚𝑎𝑥)𝑙𝑎𝑚 = 𝑑2 −𝜌𝑜

18𝜂 𝑔 (7)

(𝑣𝑚𝑎𝑥)𝑡𝑢𝑟𝑏 = √4

3𝑑−𝜌𝑜

𝜌𝑜𝑔 (8)

can be obtained for both flow patterns with the application of dv/dt = 0 as the boundary condition.

In order to make a choice between the above two formulae, the flow conditions around the particle

moving in the medium should be known. It can be characterised by the dimensionless Reynolds-

number:

𝑅𝑒 =𝑣𝑑𝜌𝑜

𝜂 (9)

where d is the diameter or the characteristic size of the particle. The dynamic viscosity of the

aqueous medium – with a good approximation – is 0.001 Pas, and the density can be taken as 1000

kg m-3. The flow around the particle is fully laminar if the Re value is less than approximately 0.2

and it is fully turbulent if this value is above approximately 800. According to formula (9), the

laminar flow is exclusive if the relative velocity is lower than 210-4 m/s and it is turbulent if the

velocity is higher than 0.8 m/s. In the velocity range between these critical values, the flow pattern

is mixed. The critical velocities change inversely with the diameter of the particles. Thus the

formula (7) referring to laminar flow conditions may apply only for very finely ground (< 100 µm)

particles of densities similar to that of the medium. The formula (8) referring to turbulent flow

conditions may be valid for large (> 1 mm) particles of densities significantly different from that

of the medium. In cases mostly referring to practical conditions, it is difficult to give a theoretically

correct solution to the maximum relative velocity of the particle. The Rittinger correction factor

[17] is applied in practice in the argument of the formula (8) corresponding to turbulent flow

conditions, whose value is 2.5 under the usual conditions of mineral processing. The usual flow

pattern is thus complex even for spherical particles, but the actual shape of the particles should also

be taken into consideration. Spherical particles may move significantly faster than flat ones in the

medium. If the shape is very different from a sphere, the characteristic linear size of the particle

39

may be given as the diameter of a sphere of equal volume or equal perpendicular cross section.

Then the drag force in formulae (2) and (3) should be completed by including also a shape factor.

The particles of different sizes, shapes and densities move with different velocities in

aqueous media. This is the principle of sedimentation (settling), which is the simplest and most

traditional separating procedure. It has been applied by the prospectors for the separation of gold

particles from the alluvia of rivers. They had to wash tons of sand in small batches in their large

conical bowls (riffles) to separate a few grams of gold particles in the best cases. During the gentle

stirring, the heavy particles accumulated at the bottom and the lighter sand particles could be

removed by decantation. This method has been developed to an industrial scale resulting in the

semi-continuous or continuous techniques of separation where the fine material is slurried with

water and streamed continuously above a rugged surface keeping the heavy particles and the light

fraction is washed away. A typical modern equipment - used in mineral processing and in

hydrometallurgy - applying sedimentation is the Dorr-thickener, which is a shallow conical basin

of a few tens of meters in diameter (Fig. 18), which – in an extreme case - can settle even the finest

particles. The settled sludge is moved slowly by a rabble mechanism towards the outlet at the centre

of the bottom cone, from where it is removed by pumping. The liquid phase, clarified according to

the set parameters, can be run off through the overflow for recycling or discharging.

Fig. 18. The schematic structure of the Dorr-thickener (A – thick sludge, B – liquid phase).

40

The settling characteristics can be modified by the controlled counter flow of the aqueous

medium. The rising flow of the medium can be controlled so as the maximum settling velocity of

the particles to be settled is higher than the velocity of the stream. The lighter sludge may be further

classified in a subsequent unit with a slower counter flow. The liquid medium can be replaced by

air. This method can also be used for the size analysis of small particles, which cannot be measured

by sieving. A special implementation of settling is in a pulsing medium, where the thick sludge is

fed on a grille through which a pulsing piston pushes the water as fast as to suspend the layer.

During the back stream the particles settle according to their specific characteristics. Particles of

high density can be collected from the grille surface, and the gangue particles of usually low density

are removed by overflowing above a baffle. The third fraction consists of the fine particles crossing

the grille.

Efficient classification can be produced with small dimensions of the apparatus in cyclones.

The medium may be gaseous or fluid. In the latter case, the slurry is fed at a high speed into the

conical “hydrocyclone” equipment (Fig. 19) tangentially at the top.

Fig. 19 Schematic of the cyclone apparatus (1 – input slurry, 2 – thick sludge, 3 – thin overflow).

The shape of the apparatus forces the high-speed flow to a spiral path which generates vortex and

a rising flow in the middle too. The thin medium leaves through the vortex finder, a central outlet

pipe, while the thick sludge is discharged through a control valve at the bottom. Particles carried

by the whirling medium get to different trajectories according to their mass, while they are also

settling. The lighter particles get into the centrally rising flow, thereby separated from the heavier

ones settling peripherally. The characteristics of separation can be modified by adjusting the flow

rate. Although the space requirement and the initial costs are relatively low, the wear of the sludge

41

pumps means considerable burden, and the maximum particle size in the sludge may be 2 mm. The

favourable solid concentration is near the lower value of the usual 25 – 50 % (V/V) range applied.

As the separation also depends on the size and shape of the particles, the thick sludge obtained at

the bottom may also contain lighter but larger gangue particles, which can be separated in a

subsequent step.

However, the relatively coarse particles of the heterogeneous ground material can also be

separated merely by their different densities by settling in heavy suspension media. A simple

conical equipment suitable for this operation is schematically shown in Fig. 20.

Fig. 20 .Heavy suspension separator with chain belt discharging of the dense material.[17]

The particles consisting of the valuable metal compounds have usually a density of approximately

4 g/cm3 while the density of the most common silicate gangue minerals is rarely higher than 2.5

g/cm3. If the density of the fine suspension is set between these two values, the lighter particles

consisting mostly of the gangue minerals are floating to the surface, while the valuable particles

made up of mostly the valuable metal oxides or sulphides settle. A heavy medium of that high (3

~ 3,5 g/cm3) apparent density can be prepared in a stable way by dispersing the finely ground (100

-200 µm) heavy materials (usually baryte magnetite or ferro-silicon) in water. The material of

higher density than that of the aqueous suspension settles to the bottom of the container from where

the discharging mechanism removes it. The particles of lower density are washed out by the

overflowing suspension. The difficulty implied is the stabilization of the medium because additive

particles get lost into both the concentrate and the gangue. Nevertheless, this is one of the cheapest

technique for separation and concentration.

42

Another relatively simple separating technique that can be implemented at low cost, is the

use of shaking tables. The ground raw material is fed in a water slurry- of approximately 25% -

solids to a large deck, whose surface is riffled (with elevated ridges) perpendicularly to the feed

and is mounted slightly tilted forward and sideways. The slurry travels longitudinally, while the

table is shaken longitudinally. The distance of the reciprocal table movement (of a few Hz

frequency) can be adjusted within a few centimetres, and it is faster on the reverse than on the

forward stroke. The particles are traveling with the forward flow of the liquid medium and across

along the riffles. As a result of shaking, the higher density and smaller particles get below the

lighter and larger ones, thus the flow can wash the latter over the riffles towards the tailings

discharge side of the table. The heavy and small particles travel across the table directed by the

riffles. Due to the mixed effects, different particles will leave the table at different points. In order

to restrict the separation to the differences in the specific densities, it is worth classifying the

material according to particle size before feeding.

The magnetic properties of some valuable minerals can also be utilized for separation. Such

examples are magnetite (Fe3O4), pyrrhotite (FeS). Other oxidised iron minerals can also be

transformed into magnetite by heating under controlled conditions or some chemical methods.

There are also some definitely paramagnetic minerals, like siderite (FeCO3), chromite (FeCr2O4),

ilmenite (FeTiO3), or franklinite (ZnFe2O4), whose magnetic separation is also possible but at

least one order of magnitude stronger magnetic field is to be applied than in the case of the ferro-

magnetic minerals. The magnetic particles will stay in the magnetic field of the equipment shown

in Fig. 21a, thereby getting separated from the non-magnetic particles moving on a gravity path.

Fig. 21 Dry (a) and wet (b) magnetic separators. [17]

a) b)

43

The relatively coarser grained raw material can be processed better in a dry state, but the fine

material obtained from wet grinding can be treated also directly, thus the cost of drying can be

avoided. The magnetic particles of the slurry fed into the tub of the wet magnetic separator (Fig.

21b) will attach to the rotating drum as long as the surface is over the magnet. Later on the particles

drop into the discharge launder outside the tub. Both versions of magnetic separators can be applied

efficiently and economically.

In order to separate the finely ground particles containing characteristically different

components, the widely variable electric conductivity of the minerals can be also of use. Figure 22

illustrates the working principle of the electrostatic separator utilizing the differences in

conductivity. The particles in the feed receive electric charge from the crown electrode then in

contact with the earthed rotating drum, the good conductors lose their charge and fall down from

the rotating drum under the effect of gravity. However, the non-conducting particles stay longer

attached to the surface of the drum and finally a mechanical force or a contrary charge can detach

them to fall down at a farther point.

Fig. 22 Schematic of the electrostatic separator.

If the material is multiply heterogeneous, the particles of different conductivity can be collected in

multiple vessels placed side by side. A precondition of separation is the supply of the material in a

thin layer and assuring dryness which limits conductivity to the material of the particles.

44

3.4.2 Separation by surface properties

Flotation is the most common and most often used method of ore beneficiation. The mechanically

liberated particles of the raw material can be executed by the different surface properties of the

constituting minerals. The valuable minerals are usually hydrophobic, or they can be made that by

applying suitable reagents. Thus they tend to be covered by the bubbles of the injected and

dispersed air, which carries them up to the stabilized froth at the surface of the slurry. The

processing of complex ores may imply the separation of the different valuable mineral particles

beyond the removal of the gangue. The finely ground raw material is fed into a flotation cell,

depicted in Fig. 23. The particles consisting of predominantly the valuable minerals are lifted by

the attached air bubbles and are discharged with the overflowing froth. The predominantly gangue

particles simply settle to the bottom from where they can be removed as sludge. The required high

degree of concentration can be achieved by repeating the treatment in consecutive steps, while the

metal recovery can be still acceptable.

Fig. 23 Schematic of the Denver flotation cell.[17]

As the surface properties of the valuable and gangue minerals may not differ enough for an

efficient separation, it is usually assisted by the addition of a selectively chemisorbed organic

reagents to collect the valuable particles. These substances are surface active, their molecules are

composed of a long apolar alkyl chain and a polar (carboxyl, hydroxil, sulphydril, amino) radical.

45

The hydrophobic character can be produced most often by the di-thiocarbonate (xanthate)

molecules, especially at the surface of the sulphide mineral particles. Among them the potassium

alkyl xanthate or di-thiophosphate salts are commonly used for ore beneficiation.

(10)

The least expensive is the compound containing ethyl group, but for higher efficiency, homologues

containing more carbon atoms can also be applied. These compounds are ionized by electrolytic

dissociation in the aqueous medium and can be bound to the ions of opposite charge formed at the

surface of the valuable mineral particle. The bond is created by the substitution of the metal ion in

the crystal lattice of the mineral by potassium. The effect of the di-thiophosphates is weaker,

therefore they are useful in multi-step selective procedures, when the easier floated components

are separated with this reagent, and then the remaining useful component is collected with

xanthates.

The formed heavy metal salt becomes practically insoluble and the organometallic

compound is fixed to the surface of the crystal. The alkyl group of the bound organic molecule is

oriented perpendicularly outwards. If the coverage is satisfactory, the surface of the particle shows

already the characteristics of the hydrocarbons, and it forms a small contact angle (θ) with air and

a large one with water, as illustrated in Fig. 24. This is the way to make it hydrophobic and to

surround it with air bubbles.

Fig. 24. The formation of the hydrophobic characteristics allowing the flotation of the particle.

O CxH2x+1 S = C S K

K S CxH2x+1 P S CyH2y+1

46

The contact angle of water is much less than 90o for the clay minerals and for the most oxides or

hydroxides (sometimes approaching 0o), therefore these minerals are hydrophilic and are well

wetted. On the other hand, when the surface tension of the liquid against the solid material is large

and its contact angle is larger than 90o, the particle is not wetted, rather it tends to be covered by

the gas phase. However, even in the cases of the least wetted surfaces, like wax, the measured

contact angles only approach 120o. This value is reached by the mineral particles if the potassium

ethyl-xanthate molecules almost fully cover their surface. However, the surface active additive can

never produce a complete coverage. The contact angle can be increased in practice by increasing

the concentration of the collector reagent or by applying a more efficient one. The former method

is efficient only to a certain limit because the overdose of the reagent decreases selectivity and by

flocculation of the fine particles, it may also cause unwanted settling. The latter method may be

beneficial depending on the costs. However, a moderate ability of flotation may be enough if the

gangue minerals are well wetted and can be settled. The efficiency of the collector reagent is

strongly influenced also by the oxidation of the surface. A certain level of oxidation of the

sulphides may even be beneficial through the generation of the suitable surface charge, but stronger

oxidation may make flotation impossible. Another important condition is the particle size of the

raw material. The usual range is 50 ~ 300 µm, but the ideal diameter also depends on the density.

A narrow size range should be assured after grinding, avoiding too large particles, but also the

extremely fine sludge. The density of the slurry and the concentration of the usual additives are set

in preparatory tanks equipped with intensive stirring. In the first step, the usual solid content is

approximately 50%, but in subsequent steps it may be significantly lower.

Besides the collector reagent, some other additives may also be required. The most

important modifying reagent is the alkaline or acidic pH regulating additive. In order to assure the

flotation of the valuable mineral, the pH must be kept under a certain maximum value, so as the

hydroxyl ions should not displace the molecules of the collector reagent. Controlling the pH may

be used also to create differences among the flotation of the mineral components. Besides

alkalization, there are some depressor agents, which can prevent the flotation of certain minerals

by similar surface reactions. On the other hand, minerals that are difficult to treat can be activated

by preferential surface reactions.

A generally needed reagent consists of a long apolar section and a polar ending oriented

towards the aqueous phase, stabilizing the froth at the surface of the slurry with which the collected

47

particles can be transported out of the cell. The apolar parts of molecules projecting out

perpendicularly from the film layers of the bubbles repel one another, therefore enhancing stability.

However, the froth stabilizer does not modify the surface of the mineral, therefore, it does not

influence the controlled selectivity of the operation. Further, it is also required that the froth should

collapse and release the discharged particles after it is laundered from the cell on the effect of water

spraying. Most of the detergents and soaps are too strong frothers. Instead, the well-known pine oil

and other synthetic additives are used for this purpose. The stabilized froth’s structure is not

homogeneous. The tiny bubbles leaving the slurry rise in the froth layer and merge, or break up.

The volume in the liquid films of the growing bubbles is decreasing, and the excess liquid flows

back to the slurry. In the meantime, it washes and returns the less stable – predominantly very fine

– gangue particles. Because of this post-cleaning effect, the timing of the froth removal and

decomposition may also be important.

3.5 Separation from the matrix phase

The solid particles can be separated from the liquid medium by filtration after thickening. For

the utilization of the filtration capacity, it is worth decreasing the water content of a thin slurry to

approximately 50% with a Dorr-thickener (Fig. 18) or with a hydrocyclone (Fig. 19). More water

can be removed from the thick slurry (or sludge) by driving it through a dense filtering cloth. This

can be enhanced greatly by applying pressure in a batch process, or less efficiently, but

continuously with the application of vacuum. The typical apparatus is the vacuum drum filter,

with which a final water content of 5 – 10 % can be achieved. The filtering cloth, made of a suitably

dense and proper type of material is fixed on the perforated surface of the rotating drum, composed

of vacuum compartments. Water from the slurry fed into the trough is sucked to the main suction

chamber inside the drum, from where it is discharged axially. At the opposite side, there is an

auxiliary suction chamber for the rinsing water which is fed to the layer at the top of the drum.

Finally, the filter cake adhering to the surface of the cloth is removed by an inserted sharp scraper

blade to be stored in as container.

48

Fig. 25 Schematic of the vacuum drum filter.

A similar procedure is the gas cleaning, the precipitation of flue dust from a stream of gas.

The first step is the rough settling of the particles by introducing the gas stream into a larger space,

where gravity and direction change are the main effects. Subsequently, for a more efficient

cleaning, the gas is directed into a cyclone apparatus (Fig. 19), which has a narrower inlet smaller

diameter in the case of a gas medium. To remove the remaining dust, it is possible to apply

electrostatic precipitation (ESP), where the small electrodes of negative charge ionize the passing

gas, and the generated ions are attached to the dust particles. The charged particles are attracted by

the large vertical electrodes connected to earth and they are collected in discharge troughs at the

bottom of the chamber. The efficiency of electrostatic precipitation can be very high (~99.99%)

and it can be operated easily and inexpensively, but it has high investment costs. Filtering can also

be applied also for the gas medium. Solid particles can be removed from the gas also by applying

filter bags made of fine cloth material. The smallest particles cannot penetrate the dense layer of

dust collected at the surface of the bags, which gives special efficiency. The total filtering surface

is increased by installing many parallel bags of several meters in height and about only 15 cm

diameter in the bag chamber. The building up of too thick layers are prevented by periodically

reversing the gas flow, and the dust is shaken off into the collecting bunker at the bottom of the

chamber. If the gas is humid or hot, the electrostatic devices can be used. The removable particle

sizes are 100 µm with gravity gas cleaning 10 µm with cyclones, 1 µm with bag filters and even

smaller with ESP.

49

3.6 Agglomeration

Concentration requires the preliminary mechanical liberation of the material by fine grinding, thus

the concentrate consists of very fine powder. This material cannot be treated in such a metallurgical

equipment where the particles in a large mass of static feed material have to be contacted with a

gaseous reagent. The compacted particles cannot offer the required interfacial surface for the

heterogeneous reaction. For an efficient process, the powder should be transformed into porous

pieces that can provide the required large specific surface also in the stacked material. The

agglomeration of the fine particles, the transformation of the powder into porous chunks can

be executed at low temperatures by briquetting or pelletizing, or at high temperatures by sintering.

A combination of pelletizing followed by sintering is also possible. The former works properly

only with fine powder raw material, while the latter requires coarser particles to be fed. During

sintering, the physically and chemically bound water content is removed, compounds may

decompose and react with the added reagents, which may enhance the reactions of the sinter at the

subsequent smelting operation.

3.6.1 Pelletizing

The simplest and cheapest way to produce the practically required particle size from the fine

(usually < 50 µm) powder is by the bonding that is based on the capillary and surface forces

arising from the moisture content. However, this bonding must also be assisted by a slight

compression that can be provided by the pressure from the inherent weight of the suitable

moistened particles in a rotating drum or disc set up with a tilted (5 – 10o) axis. Therefore, setting

the correct feeding rate of the raw powder and the rotation speed (usually 10 – 20 per minute) are

also important parameters besides the accurate controlling of the moisture content. The produced

pellets are usually dried and classified with a 10 mm screen and the smaller ones are recycled. The

pellets may be further strengthened by a recrystallizing or – by the addition of agents – vitrifying

treatment at high temperatures.

The moisture content of the raw material is 5 -10 %, while special binder – e.g. bentonite –

may be also added. As shown in Fig. 26, there is a binding force acting through the points of

contact of two spherical particles of the same (d) diameter in the direction of the centres. This can

be expressed by the surface tension and the decrease of the hydrostatic pressure [17]:

50

𝐹 = 2𝜋𝑏𝜎 + 𝜋𝑏2𝜎 (1

𝑐−

1

𝑏) =

𝜋𝑑𝜎

1+𝑡𝑔𝜃

2

(11)

where is the surface tension of the liquid, b is the radius of the imaginary circle involving the

moisture bridge and the line between the centre points, c is the radius of the arc formed at both

sides of the moisture bridge and θ is the curve angle.

Fig. 26 The moisture bridge binding two spherical particles together.

The binding force is proportional to the diameter of the particles and to the surface tension, and

according to the decrease in the liquid volume, i.e. with smaller curve angles it increases to the

value of πd. However, with little moisture content, the bridge can withstand little deformation

before breaking, so the pellet becomes brittle. With more liquid, the binding force is weaker, but

as the particles move apart, the curve angle decreases and the force increases, which gives

flexibility to the bond. The smaller and well wetted particles can strengthen the pellet, but dissolved

electrolytes can reduce the necessary surface tension.

3.6.2 Sintering

The strong but not dense binding of the small particles in larger pieces of the material can be

provided by high temperature sintering treatment, resulting in a diffusion at the contact points of

51

the particles. The process takes place below the melting point. This especially required before

reduction smelting in a shaft furnace where the powdery material would stop the essentially

important gas flow in the vertical shaft. Sintering means the formation of solid bridges around the

contact points of the particles. This is driven by the relative flattening of the strongly curved

surfaces of high energy. The material is shrinking with the partial merging of the particles. The

change in the physical state may be accompanied by significant chemical reactions too at the

applied high temperature. The crystal growth of the new compounds formed by the chemical

reactions at the touching surfaces is another important factor in the processes resulting in the joining

of the particles.

The extraction of non-ferrous base metals is often carried out by pyrometallurgical

technologies at high temperatures from sulphide ores. In this case, the high temperature pre-

treatment has another goal too. The sulphide concentrate has to be oxidised to a certain degree.

This is carried out by sintering if it is followed by smelting in a shaft furnace. The usual continuous

industrial implementation for this purpose is the Dwight-Lloyd sintering machine, as shown in Fig.

27. The raw material is charged on the surface of the moving grate, and the heat is generated by

the oxidation reaction of the suitable component with the air sucked through the layer. Therefore,

it is important to assure gas permeability throughout the procedure. It can, however, be hindered

by the excessive melting of the material as a result of overheating. It is one of the reasons why the

moisture content of the material has to be set accurately before charging.

As the oxidation of sulphide materials is usually strongly exothermic, sintering can be

thermally autogenous. Too much heat may however cause unwanted melting, which would

diminish the active surface area and hinder the passage of the air or even block the process.

Overheating can be averted by recycling the fines obtained at the crushing of the oxidised sinter.

At the same time, however sintering is assisted by the partial melting of the particles, and the

temperature can rise only temporarily, because after the reaction zone has passed, the aspirated

cold air quickly cools down the heated layer. On the other hand, as the reaction zone is approaching,

a reducing gas mixture meets the surface of the particles, and some metallic phase can also be

formed. However, after the reaction zone has passed, fresh air arrives here, and the re-oxidation

forms new crystals, which strengthen the bonds joining the particles. A similar effect results from

the formation of complex compounds by the softening or melting of the accompanying oxides

52

during the arising temperature peaks. If fine powdery material is to be treated, a preliminary

pelletizing may be necessary before sintering.

Fig. 27 Schematic of the Dwight-Lloyd-type sintering machine.

The temperature is changing along the length (approx. 20 – 100 m) of the machine and in the depth

(approx. 300 – 500 mm) of the layer because of the moving surface and the sinking reaction zone.

Instead of the highly productive but expensive continuous machine, the batch operated Greenawalt

pan – working on the same principle - can also be a satisfactory technical solution.

In the case of sulphide concentrates – characteristic of the non-ferrous base metals – the

double task of sintering, applied before smelting in shaft furnaces essentially implies the

modification of the chemical composition besides the physical state. The sulphide content of the

concentrate may be converted either fully or partially to oxides. This requires intensive solid-gas

heterogeneous reactions. For this purpose, the high specific surface is assured by the porosity of

the material and the heat is provided by the oxidation reaction. All these conditions can be provided

with the properly prepared sulphide concentrates, however, if the material consists of thermally

inert oxides, heat must be supplied by other oxidation reaction. For this purpose, the raw material

can be mixed with sufficient amount of coke powder. In the case of carbonate ores, thermal

decomposition at high temperatures even consumes heat, while converts the material into oxide

form. Depending on the type of the involved chemical reactions, the exhaust gas contains different

levels of sulphur dioxide and carbon oxides besides the ballast nitrogen and the remaining oxygen.

The dust content of the gas has to be eliminated by the usual gas cleaning technologies before it is

53

exhausted through the stack. The required properties of the sinter (satisfactory strength, still

crushable, chemical reactivity, permeability, large specific surface) can be assured only by

optimizing the sintering procedure.

3.6.3 Briquetting

A simpler mechanical method of agglomeration is briquetting, where the fine powder is mixed with

the necessary amount of water and - if necessary - with binder additives, then applying high

pressure, shaped pieces of the raw material are produced. These steps are followed by a drying and

hardening heat treatment. The size of the briquettes may be increased to the optimum, in view of

its decreasing effect on both the costs and strength.

4 Metallurgical thermodynamics

The primary goal of chemical metallurgy is the extraction of metals from different kinds of raw

materials. In order to assess the possibility of the designed processes, to examine the implied

materials and heat balances, the equilibrium conditions of the underlying reactions should be

determined. This is also possible even without specific experiments by thermodynamic

simulation, applying the databases created on the basis of calorimetric results collected in several

decades. By applying the thermodynamic functions, the equilibrium distribution of the components

can be determined in the system. For this purpose, it is indispensable to know the fundamental

thermodynamic characteristics of the reagents and the assumed products, as well as the conditions

determined by the main parameters, such as the temperature, the pressure and the concentrations.

Reactions will happen so that the equilibrium state is approached. Discussion of chemical

metallurgy assumes that the principles of physical chemistry – an in this specific respect - the

thermodynamic functions are known. The examination of reactions is based on this and also on the

application of databases available in printed or electronic forms [19Kubaschewski, O., Alcock, C.B.:

Metallurgical Thermochemistry, Vol. 24. International Series on Materials Science and Technology, , Ed. Raynor,

G.V., Pergamon Press, 1979.; 20JANAF Thermochemical Tables Third Edition. M. W. Chase, Jr., C. A. Davies, J. R.

Downey, Jr., D. J. Frurip, R. A. McDonald, and A. N. Syverud. J. Phys. Chem. Ref. Data, Vol. 14, Suppl. 1,1985.]

54

4.1 Gibbs free energy and activity

Although the subject of chemical metallurgy is discussed assuming the basic knowledge of

physical chemistry, including the thermodynamic functions of state, it is still useful to review the

principles and correlations describing the reactions in chemical metallurgy. Thus the possibilities

of transformations and the characteristics of equilibria can be examined.

The concept of thermodynamics is based on the first law, stating that in a closed system (where

the amount of the material is constant) the sum of the transferred heat (Q) and the external work

(-pV) results in the change of the system’s internal energy (U). According to the sign convention,

both factors are considered positive if they increase the internal energy of a substance. Heat

transferred reversibly and at constant pressure – as usual – may result in the change in the internal

energy and thermodynamic work. Enthalpy is an abstract concept, which is related to the internal

energy, but it also involves the product of pressure (p) and the volume (V) of the material:

𝐻 = 𝑈 + 𝑝𝑉 (12)

According to the first law of thermodynamics, the change in the enthalpy at constant pressure

(H)p equals the heat (Q) exchanged by the substance. As a result of the transferred heat, the

entropy of the matter (disorder in the movement of the particles) is also increased. Its value is

determined by dividing the transferred heat with the temperature (T) of the reversible process:

𝑑𝑆 =𝑄

𝑇 (13)

Heat transferred to a mole of a material can be expressed by the molar heat capacity (C) and the

change in temperature (dQ = C dT), whereas the change in the entropy is obtained by dividing it

with the actual temperature (dS = 𝐶

𝑇 dT). In heat exchanges at constant pressure – as in the most

frequent cases - the molar heat capacity at constant pressure (Cp) is greater than that (Cv) at

constant volume of the system, as the expansion of the heated material also has to exert work on

the environment. For a finite change in a wider temperature range, the dependence of the heat

capacity on temperature has to be taken into account. Therefore, the heat effect can be expressed

by the integration of the heat capacity over the temperature range. Additionally, latent heats of

55

transformation also arise at certain temperatures, where the material suffers transformations in its

physical state. In this case, the heat of transformation means the change in the enthalpy and the

change in the entropy can be expressed by dividing it with the temperature.

The second law of thermodynamics determines the direction of the spontaneous processes,

stating that in practice, the entropy of the isolated system – i.e. the examined material and its

surroundings within which the exchange of matter and energy is possible – is increasing. The

application of this principle is not simple, as the surroundings have to be taken into account too.

To determine the direction of the processes taking place under the usual conditions of constant

pressure, it is more practical to use the Gibbs free energy, or as it can also be referred to, the free

enthalpy (G) referring to the materials in the examined system:

𝐺 = 𝐻 − 𝑇𝑆 (14)

It is decreasing in all spontaneous processes. In case the process takes place at a constant

temperature, the finite change of the free enthalpy:

𝐺 = 𝐻 − 𝑇𝑆 (15)

This indicates the amount of useful work that can be gained from the process at constant pressure.

The part of the change in the total internal energy related to the change of the entropy is not

available for utilization. In a spontaneous process, the change in the free enthalpy of the system is

negative, that is, the system is capable of performing useful work. This may result from an

exothermic effect (H < 0) at constant pressure or from the tendency to increase entropy (TS >

0). The result of these two effects determine the direction of processes.

For practical reasons, it is worth applying the convention of standard enthalpies (heats)

of formation and the changes in free enthalpies computed on this basis. The standard enthalpies

of formation are considered as zero for the elements. However, the enthalpy of formation of a

compound corresponds to the change in the enthalpy as a result of its formation from the elements.

In this way, the thermodynamic characteristics of all the reactions can be computed, as the elements

are not transformed and they are not broken further down in chemical transformations, which

happen among the elements and their compounds.

56

By combining Equations (12) and (14), the infinitesimal change of the free enthalpy can be

expressed as:

d𝐺 = d𝑈 + 𝑝d𝑉 + 𝑉d𝑝 − 𝑇d𝑆 − 𝑆d𝑇 (16)

According to the first law, the infinitesimal change in the internal energy can be expressed as:

dU = Q – pdV (17)

where – according to Eq. (13) as the definition of entropy - the reversible heat effect at a constant

temperature is Q = TdS. Thus, expression (16) can be simplified as:

d𝐺 = 𝑉d𝑝 − 𝑆d𝑇 (18a)

or if the temperature is constant:

(d𝐺)T=const. = 𝑉d𝑝 (18b)

According to the change in pressure (pk initial, pv final) at constant temperature, the change in the

free enthalpy of the matter can be derived as:

𝐺𝑇 = ∫ 𝑉d𝑝𝑝𝑣

𝑝𝑘 (19)

Further on, the constant temperature is marked by not italicising its (T) symbol. Applying the ideal

gas law (pV = nRT) for one mole (n = 1) of material in the ideal state, the change in the molar free

enthalpy is:

𝐺 = RT∫d𝑝

𝑝

𝑝𝑣

𝑝𝑘= 𝐑Tln

𝑝𝑣

𝑝𝑘 (20)

If the initial state corresponds to the standard conditions, where the partial pressure of the matter

is atmospheric (p), the free enthalpy of the matter in the actual state can be expressed as the sum

of that under the standard initial conditions and the change in reaching the actual state is:

57

𝐺 = 𝐺∅ + 𝐺 = 𝐺∅ + 𝐑Tln𝑝

𝑝∅ (21)

The form of the expression would not be so simple for real gases, where a perfect theoretical

correlation cannot be found between the pressure and the volume. Therefore, keeping the simple

form of the expression, an abstracted value of the pressure, the fugacity (f) is substituted, whose

value may deviate from the partial pressure. Thus, Eq. (21) can be rewritten for real gases as:

𝐺 = 𝐺∅ + 𝐑Tln𝑓

𝑓∅= 𝐺𝑜 + 𝐑Tln

𝑝

101325 Pa (22)

Fugacity can be obtained from the partial pressure with the fugacity coefficient (f = p) on the

basis of experiments (or from published data referring to the given conditions). The partial pressure

is close to the fugacity in real gases at low pressures and high temperatures. Activity is considered

as the ratio of fugacity to its standard value.

In ideal solutions, the concentration of the solute is related to its partial pressure above

the solution, as stated by Henry’s law. Therefore, the concentration of the solute in the actual (c)

and the standard (c∅) states may be used instead of the pressure in Eq. (22), yielding:

𝐺 = 𝐺∅ + 𝐑Tln𝑐

𝑐∅ (23)

The standard concentration is of unity, so in an ideal system, the free enthalpy can be written as:

𝐺 = 𝐺∅ + 𝐑Tln𝑐 (24)

In real systems – with similar abstraction as introduced with fugacity – the concentration can be

replaced by activity (a), which is related to concentration through the activity coefficient (a =

c). In this case, the activity of the matter is unity in the standard state, and the free enthalpy can

be expressed as:

𝐺 = 𝐺∅ + 𝐑Tln𝑎 (25)

58

If the matter is in standard state and its activity is unity, with RTlna = 0, Eq. (25) returns the

standard free enthalpy value (G∅). The value of activity approaches that of the concentration in

dilute solutions. In different systems the activity of the examined solute depends on its own and

other components’ concentrations in various ways. The activity functions based on experimental

or simulation results can be found in relevant publications or – in some cases – in specific

monographies. [21Zemaitis, J.F., et. al.: Handbook of Aqueous Electrolyte Thermodynamics, New York, American

Inst. Chem. Eng. Inc., 1983.]

4.2 Physico-chemical equilibria in chemical metallurgy

All thermodynamic approaches applied for the examination of chemical metallurgical

processes aim at determining the equilibrium conditions of reactions producing the metal or its

compound. The system always tends to approach equilibrium, but a continuous operation requires

assuring the conditions significantly different from that, which is achieved by setting suitable

physico-chemical parameters and concentrations. Processes happen in material systems where the

relative amount of each matter changes as a result of the reaction. The resulting distribution of

matter is expressed by the equilibrium constant. According to the mass action law, established by

Guldberg and Vaage still in the 19th Century based on kinetic consideration, in the generalized

reaction of four components (A,B,C,D):

AA + BB = CC + DD (26)

the equilibrium constant (Kx) can be expressed with the concentrations - mole ratios (xi) – and the

stoichiometric coefficients of the participating components (i):

K𝑥 =𝑥CC𝑥D

D

𝑥AA𝑥B

B (27)

The products – usually metals or metal compounds - of reaction (26) are in the numerator and the

reagents are in the nominator. In extractive metallurgy, concerned with the recovery of metals,

59

the reaction usually refers to the production of a metal (M) from a metal compound (MmXx) with a

reagent (R):

vMmXx(~) + rR(~) = vmM(~) + tRr

tXvx

t(~) (28)

while the reagent forms a by-product (Rr/tXvx/t) compound with the radical of the metal compound.

The physical states (~) are marked in brackets after the components (which can be usually s –

solid, l – liquid, or g- gas). In homogeneous reactions the components are mixed in one phase, and

in heterogeneous reaction at least one of the components is in a condensed state.

The mass action law was later confirmed by van’t Hoff on a thermodynamic basis. This

has prime importance in examining reactions in chemical metallurgy. The change in free enthalpy

(G) resulting from the general reaction (26), can be expressed by the algebraic sum of the free

enthalpies of the components so that the products have positive and the reagents negative signs:

𝐺 = C𝐺C + D𝐺D − A𝐺A − B𝐺B = ∑ 𝑖𝐺𝑖,𝑖 (29)

Thus the sum of the values referring to the reagents is subtracted from the sum of the values of the

products. This special summation, used for reactions, is denoted by the operator “”.

According to expression (25), the free enthalpy – or, as it is also referred to, the chemical

potential – of a component (Gi) in the examined reaction is:

𝐺𝑖 = 𝐺𝑖∅ + RTln𝑎𝑖 (30)

which depends on its value referring to the standard (G) conditions and the activity of that

component matter. The standard state means the stable form of the pure matter, i.e. its activity

being unity, which is not interfered by mixing with other matter. In the case of a gas, the standard

state refers to an atmospheric partial pressure. Substituting these split formulae of the free enthalpy

into the expression (29), the following expression results:

𝐺 = C(𝐺C∅ + RTln𝑎C) + D(𝐺D

∅ + RTln𝑎D) − A(𝐺A∅ + RTln𝑎A) − B(𝐺B

∅ + RTln𝑎B) (31)

60

or:

𝑮 = 𝐺∅ + RTln𝑎C

C𝑎DD

𝑎AA𝑎B

𝐁 = 𝐺∅ + RTln𝑎𝑖,𝑝

𝑖,𝑝

𝑎𝑖,𝑟

𝑖,𝑟 = 𝑮∅ + 𝐑𝐓𝐥𝐧𝑰 (32)

where the change in the standard free enthalpy is:

𝐺∅ = C𝐺C∅ + D𝐺D

∅ − A𝐺A∅ − B𝐺

B∅ = ∑ 𝑖𝐺𝑖

∅,𝑖 (33)

and I is introduced as the activity index. In general terms, the numerator of the activity index is

the product of the activities of the components at the right side of the reaction equation to the

powers of their stoichiometric coefficients ((𝑎𝑖𝑝

𝑖𝑝)), whereas the nominator contains the activity

expressions of the reagents (from the left side of the reaction) in the same way ((𝑎𝑖𝑟𝑖𝑟)). In a

visible process, the total free enthalpy of the system changes. If it decreases, the process takes place

as assumed by the reaction equation. If, on the other hand, it would imply an increase, the reverse

reaction has the thermodynamic feasibility. Any effective process is ended when the summed free

enthalpies of the components on both sides of the reaction are equal, i.e. the change in the free

enthalpy due to the reaction becomes zero (G = 0). Thus the distribution of the matter in the

system will not change, and the equilibrium sets in. Thus the activity index in Eq. (32) becomes

constant, and it can be expressed from that equation:

𝐺∅ = −𝑅Tln [𝑎C

C𝑎DD

𝑎AA𝑎B

𝐁]equilibrium

= −𝑅Tln𝐾 (34)

The stabilized relation of the activities in the “power product quotient” (I) is indicated by the “eq”

subscript. As this value is constant at a given temperature, it is referred to as the equilibrium

constant expressed with the activities. Substituting it back into Eq. (32), the change in the free

enthalpy of a reaction can be expressed also with the activity ratios:

𝐺 = R𝑇ln𝑎C

C𝑎DD

𝑎AA𝑎B

𝐁 − RTln [𝑎C

C𝑎DD

𝑎AA𝑎B

𝐁]equilibrium

= RTln𝐼 − RTln𝐾 (35)

61

If the relation I < K is true, the reaction is thermodynamically possible in the assumed direction. In

the opposite case, the reaction may proceed in the reversed direction. Reactions may take place as

long as the equilibrium conditions are reached and they naturally tend in this direction. For devising

chemical metallurgical processes, it is a fundamental task to determine the equilibrium constants

for the required temperatures. On that basis, it is possible to set such concentrations that will

allow the assumed reaction to take place. The higher the value of the equilibrium constant is, the

more likely it is that the reaction will proceed in the assumed direction, from left to right as written

in the equation as long as the accumulation of the reaction products and the consumption of the

reagents make the value of the activity index (I) grow and finally reach the value of the equilibrium

constant (K).

The expressions above involve the activities, although in practice we may only calculate

with concentrations or – in the case of gases – with partial pressures. In real systems, activities may

significantly deviate from the relevant concentrations. The activity coefficient providing the

relationship between them can be obtained from experiments at the set temperature in a given

system. Activity coefficient functions determined from experimental results and often assessed by

simulation are available is specific literature.

4.3 The effect of temperature on the characteristics of the reaction

Besides the nature of the components and the distribution of concentrations, temperature has a

major influence on the feasibility of reactions and the on the equilibria of transformations. This

effect can be determined experimentally too, but the thermodynamic approach offers the possibility

of deriving generally valid relationships. Concerning the extraction of metals, the processes of

reduction/oxidation have paramount importance. The critical reaction is most often the formation

and the decomposition of the metal oxides. The former is usually exothermic and the latter is

endothermic. The heat effect – as discussed above – is in relation with the feasibility of the

reaction. It also has a general influence on the change in the thermodynamic driving force with

temperature. In order to express the latter effect theoretically, a starting point can be the relationship

(18a) for the differential and reversible change in the free enthalpy of a substance. If – as usual in

practice – the pressure is constant (p) while the temperature is changing reversibly, the change in

62

the free enthalpies of the reagents and the products (i) of a reaction is related to the change of the

temperature:

d𝐺𝑖 = −𝑆𝑖d𝑇 (p = const.) (36)

The molar free enthalpy change of a reaction results from the algebraic summation of the free

enthalpies related to the products and the reagents (ΔG = i Gi ), whose differential can be

expressed as the algebraic sum of the free enthalpy differentials of the components (i dGi).

Similarly, the differential temperature can be isolated from the algebraic sum of the products of

component entropies and the differential temperature, leading to the following expression:

dG = (d𝐺𝑖) = − 𝑆𝑖d𝑇 (p = const.) (37a)

d𝐺 = −𝑆d𝑇 (p = const.) (37b)

This expression can be differentiated with respect to the temperature, yielding:

[𝜕𝐺

∂𝑇]p=const.

= −𝑆 (38)

which is the Gibbs-Helmholtz equation. Thus the actual slope of a free enthalpy change function

of a reaction against temperature is equal to the negative of the actual entropy change. Applying

also the relationship between the changes of the entropy, enthalpy and free enthalpy of a reaction

– as expressed in Eq. (15) – the Gibbs-Helmholtz equation can be expressed in another form:

[𝜕𝐺

∂𝑇]p=const.

=𝐺−𝐻

𝑇 (39)

In order to reach an even more practical form, it is worth expressing the partial derivative of the

quotient of the free enthalpy change of the reaction and the temperature (𝐺

𝑇), with respect to the

63

temperature ([𝜕𝐺

𝑇

∂𝑇]p=const.

). This can be carried out by the mathematical rules of fractional

derivatives, as follows:

[𝜕𝐺

𝑇

∂𝑇]p=const.

=𝑇(

𝜕𝐺

∂𝑇)p=const.

−𝐺

𝑇2 (40)

where, in turn, expression (39) can be substituted to yield:

[𝜕𝐺𝑇

∂𝑇]p=const.

= −𝐻

𝑇2 (41a)

This relationship indicates that in the case of an endothermic reaction, where 𝐻 is positive, the

change in the free enthalpy becomes more negative as the temperature increases, i.e. the

thermodynamic driving force increases. Further, for the standard state:

[𝜕𝐺∅

𝑇

∂𝑇]

p=const.

= −𝐻∅

𝑇2 (41b)

Substituting Eq. (34), the temperature dependence of the equilibrium constant can be expressed in

a differential form:

[𝜕−𝐑𝑇ln𝐾

𝑇

∂𝑇]p=const.

= [𝜕(−𝐑ln𝐾)

∂𝑇]p=const.

= −𝐻∅

𝑇2 (42)

If the equilibrium constant referring to the conditions of constant pressure is denoted by Kp, a

rearrangement of this equation yields the following practical expression:

d ln𝐾p

d 𝑇 =

𝐻∅

𝐑𝑇2 (43)

64

which is also known as the van’t Hoff equation. This equation gives the change of the equilibrium

constant of a reaction with temperature at constant pressure (Kp). According to the sign of the

enthalpy change, in the case of an endothermic reaction, the equilibrium constant increases and in

the case of an exothermic reaction it decreases with increasing temperature. Thus, the reaction

changes its equilibrium constant as if it intended to stabilize the initial temperature. This is in line

with the Le Chatelier principle, i.e. a system in dynamic equilibrium changes is state to mitigate

the external effect. It reacts to preserve the value of the intensive property affected by the external

influence.

If the reaction means the reversible evaporation of a pure condensed substance, and the gas

phase of a constant total pressure can be considered ideal, the equilibrium constant is simplified to

the partial pressure of the vapour (pvap). Thus Eq. (43) becomes:

d ln𝑝vap

d 𝑇 =

𝐻vap∅

𝐑𝑇2 (44)

the differential Clausius-Clapeyron equation. If the standard enthalpy change of evaporation,

the latent heat of vaporization (𝐻vap∅ ) is assumed constant, the rearranged form of the equation:

d ln𝑝vap =𝐻vap

∅

𝐑𝑇2d 𝑇 (45)

can be integrated analytically between the boundary values of two vapour pressures and the

relevant two temperatures:

ln𝐾p,2

𝐾p,1= ln

𝑝vap,2

𝑝vap,1= −

𝐻vap∅

𝐑(

1

𝑇2−

1

𝑇1) (46)

This is the integral Clausius-Clapeyron equation, which can be used to determine the change of

vapour pressure as a result of increasing the temperature. On the other hand, after measuring the

vapour pressures at two temperatures, the equation can be applied for the determination of the

65

average standard enthalpy change of evaporation, i.e. the latent heat of vaporization referring to

the set temperature range.

4.4 Thermochemical examination of reactions

The most important point of examining reactions playing a role in chemical metallurgy is

to determine the relevant equilibrium constant. The experimental method would be difficult, and

in the cases of many possible reactions, it may be even impossible. The thermochemical approach,

however, can achieve this by computations based on the thermodynamic properties of a relatively

lower number of substances taking part in such reactions. The thermodynamic properties of the

elements and compounds most often occurring in practice are available for the extractive

metallurgist in compilations mentioned at the beginning of Chapter 4. One can find the enthalpies

of formation, the entropies and the heat capacities as temperature functions referring to one mole

of the substance in the standard state. Further, the temperatures and the heats of transformations

from one state to another. The primary objective of the computations is the determination of the

temperature functions for the standard free enthalpy changes of a specific reaction, from which the

equilibrium constants can be produced according to the relationship (34).

In numerous cases, the reactions in question can be composed by the algebraic summation

of properly selected basic reactions. According to Hess’s law, the heat effect is the same

irrespective of how many steps are combined to build up a process. As the entropy is a function of

state, it does not depend either on how the substance got into the final state. Therefore, the change

in the free enthalpy of the examined process can also be determined as the algebraic sum of the

known free enthalpy changes of the partial reactions. Some thermodynamic compilations also

contain the approximate free enthalpy change functions for the main reactions of substances in

standard state. Therefore, if possible, it is advisable to break down the examined reaction into basic

partial reactions, whose standard free enthalpy changes can be determined as functions of the

temperature individually.

Although the thermodynamic functions of the reactions can be algebraically summed, this

is not valid for the equilibrium constants, which can be determined for the resultant reaction from

the standard free enthalpy change. On this basis it is possible to determine the required

concentrations of the reagents which assures the assumed reaction.

66

4.4.1 Determining the heat of reaction

The free enthalpy of component substances in a reaction can be determined - as shown by the

relationship (14) – from the enthalpy and the entropy tags. According to the laws of

thermodynamics, each substance has a certain enthalpy and entropy in a given state. The enthalpy

change resulting from the general reaction (26) denoting the heat of reaction can be expressed in

the same form as it was shown for the free enthalpy in Eq. (29):

𝐻 = C𝐻C + D𝐻D − A𝐻A − B𝐻B = ∑ 𝑖𝐻𝑖 (47)

The heat effect of the reaction (H) shows how much heat is emitted or absorbed by the system

while the reagents on the left side are transformed into the products on the right side of the reaction

(26). The value of the enthalpy change is negative in the former case, and the reaction is

exothermic, producing heat. A well-known example is the oxidation of metals. In the opposite

case, the reaction is endothermic, indicated by a positive value of the enthalpy change, absorbing

heat from the surroundings. Most often, this is the case with the reduction of the strongly bound

metal oxides. The reaction heat can be measured with a calorimeter. Such measurements provide

the primary fundaments of the thermodynamic data bases.

The formation of a general metal compound and the associated heat is indicated by the

following equation:

𝑚M + 𝑥X = M𝑚X𝑥, 𝐻M𝑚Xx (48)

The enthalpy change related to the formation of the above metal compound – i.e. the heat of

formation – is theoretically derived from the general expression (47) as:

𝐻M𝑚X𝑥= 𝐻M𝑚Xx

− 𝑚𝐻M − 𝑥𝐻X (49)

There are the absolute enthalpies of the components at the right side of equation (49). In order to

obtain the heat of formation – enthalpy change of formation - of the noted metal compound. The

67

absolute enthalpies of the elements have to be subtracted from the absolute enthalpy of the

compound. The absolute enthalpies – heat contents – of the substances need not to be known. The

total heat content includes also the heats of formation of the atoms. However, in chemical reactions,

the nuclear energy does not change, as only the formation of the compounds from elements and

their decomposition to elements, or their transformations to other compounds can happen. Nuclear

transformations of the elements do not belong to the chemical (metallurgical) reactions.

Thermodynamics deals with the heats of chemical reactions and temperature changes, therefore,

thermodynamic data bases contain the enthalpy changes of compound formation, which is called

the heat of formation. The usual reference temperature is 298 K. At this temperature the heat of

formation (relative enthalpy) of an element is considered zero if the heats of formation are applied

instead of the absolute enthalpies for substances, referring to this temperature. Thermodynamic

computations can be carried out according to this general definition.

The role of the direct calorimetric measurements in constructing the thermodynamic data

bases can be illustrated by a concrete example[19] showing the burning of aluminium carbide:

Al4C3 + 6O2 = 2Al2O3 + 3CO2, 𝐻(50) (50)

The calorimetric result of the heat of reaction is: -4332.1 31,4 kJ/mol, referring to 298 K.

Knowing the heats of formation for aluminium oxide and carbon dioxide (-1673,6 6,3; illetve

393,5 0,4 kJ/mol), that of aluminium carbide can be calculated according to Hess’s law from the

measured heat effect of reaction (50).

𝐻(50) = 3𝐻CO2

+ 2𝐻Al2O3

− 6𝐻O2

− 𝐻Al4C3

(51a)

−4332,1 = −3 ∗ 393,5 − 2 ∗ 1673,6 − 0 − 𝐻Al4C3

(51b)

Thus the heat of formation in question is: 2𝐻Al4C3

= -195,7 (31,4 +2*6,3 + 3*0,4) kJ/mol.

The only disadvantage applying Hess’s law instead of direct measurements is the additivity of the

errors implied in the values of each component. Thus the heat of formation determined in this way

for aluminium carbide carries a relative error margin of 23 %, although the major part (~ 70%) of

it is due to the given absolute error margin belonging to the calorimetric measurement of the

68

aluminium carbide burning, although its original relative margin of error was below 1 %. Referring

to the lower absolute value obtained by the algebraic summation, the sum of the error margins

results in a significantly higher relative value. The published values in databases (- 207.3 kJ/mol

in this case) reflect the critical evaluation of multiple results.

It is not always possible to apply the direct reaction to determine the heats of formation or

heats of reactions. There are different indirect methods too. For example, calorimetry can also be

used for determining the heats of dissolution for the elements, compounds or alloys, then applying

Hess’s law, the value in question can be found by the necessary algebraic summation. Another

possible method is offered by the van’t Hoff isobar, or more precisely, the application of the

integral form of expression (43). From the values of the equilibrium constant determined for

two different temperatures at the same total pressure, the enthalpy change of the process can be

determined:

𝐻 =𝐑 ln

𝐾p,1

𝐾p,21

𝑇2−

1

𝑇1

= 𝐑ln𝐾p,1−ln𝐾p,2

1

𝑇2−

1

𝑇1

(52)

If only one gaseous component is involved in the reaction, the equilibrium constant practically

simplifies to the partial pressure of the gas, and the above relationship becomes:

𝐻 = 𝐑ln𝑝1−ln𝑝2

1

𝑇2−

1

𝑇1

(53)

where the positive sign applies if the gas component is a product and the negative is used if it is a

reagent. In the given experimental system, the measured change in a partial pressure changes the

composition of the gas phase in accordance with the constant total pressure.

As an even more indirect method, electrochemical systems may also be applied to

determine the changes in the enthalpy by a reaction. For example, in the case of the

MX + Me = MeX + M (54)

type reactions, the relationship of the cell voltage (E) with the change of the free enthalpy can be

taken into account:

69

𝐺 = −𝑧𝐅𝐸 (55)

where F is the Faraday constant (~ 96500 As/mol for ions of single charge) and z is the number

of charges exchanged in the reaction in atomic units. Applying the Gibbs-Helmholtz equation

expressed by Eq. (39) in its fundamental form, after rearrangement:

T[𝜕𝐺

∂𝑇]p=áll.

− 𝐺 = −𝐻 (56a)

and substituting expression (55), the following relationship is obtained:

H = 𝑧𝐅(𝑇d𝐸

d𝑇− 𝐸) (56b)

to describe the enthalpy change of the reaction carried out in an electrolyte solution is obtained.

4.4.2 Temperature dependence of the reaction heat

Thermodynamic databases give the enthalpy changes of formation only for the reference

temperature, for 298 K. In chemical metallurgy, however, the processes can be carried out or the

satisfactory rate of reaction can be assured very often only at significantly higher temperatures.

The enthalpy change of the reaction referring to a higher temperature can be worked out by

combining the value at 298 K and the calculated change in the heat contents of the components

between the two temperatures. To do this, one needs the molar heat capacities, which are functions

of the temperature themselves. The tables in the databases usually list the molar heat capacities

referring to constant pressure (Cp), i.e. the amount of heat (enthalpy) required for raising the

temperature of mole of the substance by 1 K (dH/dT) is given as a polynomial function of the

thermodynamic temperature:

d𝐻

d𝑇= 𝐶p = 𝑎𝑗𝑇

x𝑗 (57)

70

where aj is a constant coefficient in a term containing the temperature as the independent variable

raised to the relevant power. In the heat capacity polynomials, the first value of the xj exponent is

zero, and in further terms it is usually 2, -2 and perhaps -1/2 too. The published functions usually

consist of just a few terms, still assuring the reasonable accuracy. The relative enthalpy of one mole

of a component (Hi(T)), still in the same state but at a higher temperature than the reference value,

can be constructed from the heat of formation at the reference temperature (H298) and the heat

absorbed in the temperature interval until the set temperature is reached. The latter term is

computed by the integration of the heat capacity:

𝐻𝑖(𝑇) = 𝐻298,𝑖 + ∫ 𝐶p,𝑖d𝑇𝑇

298 (58)

Due to the polynomial type of the heat capacity function, the analytical integration can be carried

out relatively easily.

If the substance undergoes a phase or state transition in the examined temperature

interval, the integration – in theory - has to be interrupted at that point (Ttr) and the heat of

transformation (Htr) has to be added, continuing the integration with the new molar heat capacity

(𝐶𝑝,𝑖∗

) of the transformed substance:

𝐻𝑖(𝑇) = 𝐻298,𝑖 + ∫ 𝐶p,𝑖d𝑇 + 𝐻tr,𝑖 + ∫ 𝐶𝑝,𝑖∗ d𝑇

𝑇

𝑇tr,𝑖

𝑇tr,𝑖

298 (59)

Consequently, thermodynamic databases give the coefficients of the heat capacity functions for the

intervals between two adjacent temperatures of transformations and for the given phases. The

temperature profiles of the heat capacities at constant pressure [22Biswas, A.K., Reginald Bashforth, G.:

The Physical Chemistry of Metallurgical Processes, Chapman & Hall, London, 1962.] are illustrated by Fig. 28

for compounds of different states and also for a metal that suffers phase transformation in the

examined temperature range.

71

Fig. 28 Molar heat capacities at constant pressure as functions of the temperature.

The stable manganese sulphide (MnS), of high melting point, shows a steadily – even linearly –

increasing heat capacity all along the examined temperature interval. The heat capacity of CO2 at

constant pressure is increasing stronger with temperature in the lower range. The heat capacity of

nickel is increasing rather differently with the temperature in its two possible allotrope forms, and

practically remains constant in the molten state. It is evident that the changes in the heat capacity

as a result of modifications in the crystal structure and because of melting cannot be neglected by

any means. These transformations are accompanied by the transfer of significant latent heat at

constant temperature. The heats of transformations between two different crystal structures are

relatively low. The heat of fusion is higher several times, or by an order of magnitude, and the heat

of evaporation can be even higher by another order of magnitude. The most important numerical

characteristics of phase transformations are summarized in Table 6 for some metals of different

types, used in common practice.

72

Table 6. The heats of fusion, melting points, heats of evaporation and boiling points of some

practically important metals

The melting points, the boiling points, the heats of fusion and the heats of evaporation of the

chlorides are significantly lower than those of the pure metals constituting them. However, the light

alkali and alkaline earth metals are exceptional in this respect. The volatility of the chlorides is

utilized in various chemical metallurgical processes of extraction and purification. The metal

oxides, on the other hand, are characterised by higher melting and boiling points, as well as higher

heats of fusion, but metal oxides of lower valence may be more volatile (e.g. PbO, SnO, etc.).

Due to the different dependence of the heat contents of the components on the temperature,

the enthalpy change of the reactions depends also significantly on the temperature. This effect can

be taken into account by determining the heat contents of the reaction components for the given

temperature by Eq. (59). The enthalpy change of the general reaction (26) at the reference

temperature (298 K) can be transformed to a target temperature. If there is no change in the

states for any of the components until that point, we just have to carry out the following summation:

𝐻(𝑇) = C (𝐻298,C + ∫ 𝐶p,Cd𝑇𝑇

298) + D (𝐻298,D + ∫ 𝐶p,Dd𝑇

𝑇

298) − .

− A (𝐻298,A + ∫ 𝐶p,Ad𝑇𝑇

298) − B (𝐻298,B + ∫ 𝐶p,Bd𝑇

𝑇

298) (60)

or in general terms:

73

𝐻(𝑇) = ∑ 𝑖𝐻298,𝑖 + ∑ 𝑖 ∫ 𝐶p,𝑖d𝑇𝑇

298 (61)

Although it is not difficult to integrate the heat capacity functions of all the reaction components

over the given temperature interval, the method of calculation can be simplified by rearranging the

second term of expression (61) according to the distributivity of integration over polynomial

integrand. It is advantageous to replace the algebraic sum of the integrals with the integral of

the algebraic sum of the operands. This new integrand is the heat capacity change function

(Cp). Its introduction allows only one integration has to be performed between the marked

temperature limits to determine the enthalpy change of the reaction for the given temperature:

𝐻(𝑇) = ∑ 𝑖𝐻298,𝑖 + ∫ ∑ 𝑖𝐶p,𝑖 d𝑇𝑇

298 (62)

or in a shorter form:

𝐻(𝑇) = 𝐻298,𝑖 + ∫ 𝐶p,𝑖d𝑇𝑇

298 (63)

If a component undergoes some phase transformation at a temperature Ttr,k in the examined range

of temperature, the integration has to be interrupted at that point, and the absorbed heat of

transformation has to be incorporated (added for products and subtracted for reagents). Continuing

the integration for the further part of the temperature range, the new heat capacity function of the

transformed component has to be applied in a new heat capacity change function (𝐶𝑝∗) of the

reaction.

𝐻(𝑇) = 𝐻298 + ∫ 𝐶pd𝑇𝑇tr

298 𝐻tr + ∫ 𝐶𝑝

∗d𝑇𝑇

𝑇tr (64)

Another – practically easier – way is the application of Hess’s law to the partial interval above

the temperature of transformation. Considering the examined process as an overall reaction, its

enthalpy change (Hov) can be composed of the base reaction with all the components in their

original states and the reaction of phase transformation. Thus the enthalpy change of the base

reaction (Hbase) can be determined for the target temperature by the integration of the original

74

heat capacity change function for the entire examined temperature range, and in addition, the

virtual heat of transformation (Htr) obtained by the integration of the virtual heat capacity

change function of the transformation reaction over the remaining temperature range. The latter is

added if the component suffering the transformation is at the products’ side and subtracting if it is

on the reagents’ side.

𝐻ov(𝑇) = 𝐻base(𝑇) + 𝐻tr(𝑇) = 𝐻298 + ∫ 𝐶pd𝑇𝑇

298+ .

(𝐻tr + ∫ 𝐶p,trd𝑇𝑇

𝑇tr) (65)

where Htr is the heat of transformation of the transforming component at the temperature of

transformation Ttr and Cp,tr is the differential function obtained by subtracting the heat capacity

function referring to the range below the transition temperature from that belonging to the

transformed component at the higher temperature range. Thus the phase transformation, considered

as a virtual chemical reaction, can be summed with the base reaction.

The rate of heat absorption by substances during the rising temperature is illustrated by

Fig. 29, showing measured results [19] on cadmium.

Fig. 29. The change of heat content in Cd above room temperature.

75

Starting from the room temperature, accepted as reference, the heat content increases

monotonously according to the heat capacity, then at the melting point – reached early for cadmium

– the function has a step change. The height of the step corresponds to the molar heat of fusion.

Further on, the heat content of the metal melt is increasing steadily, which reflects a relatively

constant heat capacity. Melting does not cause a great change in the heat capacity functions of

cadmium, as the heat contents of both phases are increasing at the same rate.

4.4.3 The entropy change of the reaction

The entropy of a substance is changed by heat exchange or structural transformation. This

is a bound energy that cannot be converted into work, or the disorder in the system of materials is

increasing in spontaneous processes. Besides discharging energy, this is the other driving force

of reactions. The entropy change caused by heat transfer was expressed by Eq. (13). At a

constant pressure, the entropy change can be related to the change of the enthalpy:

d𝑆 =d𝐻

𝑇=

𝐶pd𝑇

𝑇 (66)

The entropy of the components of a reaction in the same state but at a temperature different from

the reference can be computed from the integral form of Eq. (66). Thus the entropies of the

components can be obtained for the target temperature by adding the increment – computed in the

same way as introduced for the enthalpy by Eq. (58) – to the reference value (S298):

𝑆𝑖(𝑇) = 𝑆298,𝑖 + ∫𝐶p,𝑖

𝑇d𝑇

𝑇

298 (67)

The analytical integration can be carried out by each term, which causes no difficulty in this case

either as the integrand is still a multi-term but simple polynomial expression, like in (57). However

instead of the constant, a term of T-1 form appears, which will have a logarithmic primitive function.

If the substance goes through a transformation of state in the temperature range, the integration has

to be interrupted at the relevant temperature of transformation (Ttr) and the entropy change of

76

transformation (Sát = Hát/Tát) needs to be added to expression (67). The integration has to be

continued with the new molar heat capacity (𝐶𝑝,𝑖∗

) of the transformed substance:

𝑆𝑖(𝑇) = 𝑆298,𝑖 + ∫𝐶p,𝑖

𝑇d𝑇

𝑇át

298+

𝐻át,𝑖

𝑇át,𝑖+ ∫

𝐶𝑝,𝑖∗

𝑇d𝑇

𝑇

𝑇át,𝑖 (68)

The ratio of the heat capacity and the temperature, 𝐶p

𝑇 means the entropy increase associated with a

temperature increase of unity, that is, the rate of the entropy increase as long as the heat transfer is

reversible. The pace of entropy increase caused by heat absorption at an increasing temperature is

illustrated by the values of the integrands in Fig. 30 for the substances also presented earlier. Since

the increase of the heat capacities with temperature is degressive, there is less change in the entropy

as the temperature is changed in the higher ranges. The phase transformations cause similar steps

as in the case of the enthalpy profile. This is illustrated schematically by Fig. 31.

Fig. 30 The pace of entropy increase as a function of temperature.

77

Fig. 31 The change in the entropy of a substance with temperature.

Considering the entropy changes due to reactions, similar formulae can be obtained as those

derived for the enthalpy change, but the integrands are the Cp/T functions instead of the heat

capacities (Cp), and the heats of transitions are to be replaced by the entropy changes of phase

transitions, which are derived by dividing the heats of transition by the temperatures of transition.

Thus the entropy change of a reaction at a given temperature is expressed as:

𝑆(𝑇) = ∑ 𝑖𝑆298,𝑖 + ∫∑ 𝑖𝐶p,𝑖

𝑇d𝑇 =

𝑇

298𝑆298 + ∫

𝐶p

𝑇d𝑇

𝑇

298 (69)

If the integration has to be interrupted because of the transformation of a component, the above

formula has to be modified by adding the entropy of transformation (with positive sign if a product

and negative if a reagent is transformed) and continuing the integration with the new heat capacity

change function, according to the analogy of the expression (64) derived for the enthalpy change:

𝑆(𝑇) = 𝑆298 + ∫𝐶p

𝑇d𝑇 ±

𝑇tr

298

𝐻tr

𝑇tr+ ∫

𝐶𝑝,𝑖∗

𝑇d𝑇

𝑇

𝑇tr (70)

78

However, it is more practical to consider the basic reaction for the entire temperature interval and

sum it algebraically to the virtual chemical reaction of the transformation, just as in the case of the

enthalpy change. It follows from Hess’s law that the entropy change of the transformation has to

be added if it refers to a reaction product and subtracted if it is for a reagent. The heat capacity

functions of the basic reactions are extrapolated to the range above the transformation temperature,

as it was proposed above in the case of the enthalpy change. Thus the entropy change of the overall

reaction (Sov) can be expressed by summing the entropy change functions of the principal reaction

and those of the virtual phase transformation reactions in a general form:

𝑆ov(𝑇) = 𝑆base(𝑇) + 𝑆tr(𝑇) = 𝑆298 + ∫𝐶p

𝑇d𝑇 +

𝑇

298 .

𝐻tr

𝑇tr+ ∫

𝐶p,tr

𝑇d𝑇

𝑇

𝑇tr (71)

where Htr is the heat of transformation of the transforming component at the temperature of the

transformation and Cp,tr is the difference of the heat capacity functions of the transforming

component pertaining to the temperatures above and below the temperature of transformation.

4.4.4 The free enthalpy change of the reaction and the equilibrium constant

The computation of the enthalpy change and entropy change values basically require the

knowledge of the enthalpies of formation and the entropies for the reference temperature of 298 K

and the enthalpies of the possible transformations, beside which the heat capacity functions are to

be known. All those data are available in the thermodynamic databases cited earlier, but they only

refer to the standard states of all the components, allowing the above formulae to be used only

by assuming all the components in their standard states. Thus only the standard enthalpy change

and the standard entropy change of the reactions can be determined on the basis of the general

thermodynamic databases. The rearrangement of the general expressions (65) and (71) and

referring to the standard states of all the components, substitution into Eq. (15) yields the standard

free enthalpy change of the reaction for a given temperature after some rearrangement:

79

𝐺(𝑇) = 𝐻(𝑇) − 𝑇𝑆(𝑇) =

= 𝐻298 + ∫ 𝐶p

d𝑇𝑇

298− 𝑇 (𝑆298

+ ∫𝐶p

𝑇d𝑇

𝑇

298) + .

{𝐻tr + ∫ 𝐶p,tr

d𝑇−𝑇𝑇tr

𝑇(𝐻tr

𝑇tr+ ∫

𝐶p,𝑡𝑟

𝑇d𝑇

𝑇𝑇át,k

)} (72)

This expression can be used generally for the computation of standard free enthalpy change of a

process. Naturally, the last row of Eq. (72) has to be considered only if the target temperature is

beyond a phase transformation, and the positive sign is applied for the expression in the braces if

the transformation happens to a product, whereas the negative sign applies if it happens to a reagent.

As a further step, after the standard free enthalpy change has been obtained, the relationship (34)

can be applied to determine the equilibrium constant for a given temperature:

𝐾 = exp (−𝐺∅

𝑅𝑇) (73)

Standard conditions are rarely characteristic of reactions, therefore the value of the standard free

enthalpy change is not suitable for assessing the feasibility, and rather the free enthalpy change –

as expressed in Eq. (35) - should be used. Accordingly, a practical criterion can be derived with

the equilibrium constant. The reaction can be expected to proceed in the assumed direction if the

activity index (I) is less than the equilibrium constant (K) of the given temperature:

𝑎C

C𝑎DD

𝑎AA𝑎B

𝐁 = 𝐼 < 𝐾(𝑇) (74)

As a first approach, the value of the activity index – according to expression (27) – may be assessed

by using the molar ratio concentrations. For more accurate computations, the activities indicated

in expression (74) are required, which can be related to the relevant concentrations by the

appropriate activity coefficients:

ai = ici (75)

80

Solid-gas heterogeneous reactions – often found in chemical metallurgy – are easier cases, as the

solid phases can be considered practically in standard states (pure and stable) while gases behave

near ideally at the usually high temperatures. Thus the activity of the pure solid components can

be close to unity, and that of the gases can be expressed according to their partial pressures,

relative to the atmospheric pressure (earlier given in atm units). So the conditions of a reaction

– defined by concentration ratios and temperatures – allowing the reaction to proceed in the

assumed direction can be outlined relatively accurately. As a numerical example, it is worth

considering the thermodynamic examination of the hydrogen reduction of copper chloride, as

introduced in the following section.

4.4.5 Numerical examination of reaction feasibility

The reduction of metal chlorides have an important role in the extraction of many metals

(e.g. Ti, Mg), but it can be useful also to reach ultra-high purity. The latter aspect can be illustrated

by a metallurgical process devised for the preparation of ultra-high purity copper [23Kékesi, T.,

Mimura, K., Ishikawa, Y., Isshiki, M.: Preparation of Ultra-High Purity Copper by Anion Exchange. Met. Maters.

Trans. B. 28B, 12 (1997), 987-993]. In this procedure, high-purity CuCl2 is produced primarily, which

can be reduced with hydrogen at elevated temperatures to yield the metal of high purity.

Application of hydrogen as a reducing agent is essential for maintaining purity [24Kékesi, T., Mimura,

K., Isshiki, M.: Copper Extraction from Chloride Solutions by Evaporation and Reduction with Hydrogen. MATER.

TRANS., JIM, 36, 5 (1995), 649-658.]. The reduction of divalent copper chloride takes place in two

consecutive steps. In general, the decomposition of compounds of multiple valence is critical in

the last step, involving the most stable form of the lowest valence. This happens also in this case.

The first step of the reduction mechanism (indicating also the physical states in the subscripts):

CuCl2,s + 1/2H2,g = CuCl,s + HCl,g (76)

is characterised by a strongly negative standard free enthalpy change even at room temperature

( - 41.6 kJ/mol CuCl2), which will be even more negative as the temperature is increased (-8,5

kJ/mol for every 100 K increment ). Accordingly, the value of the equilibrium constant is of the

81

107 order or higher. Therefore, the thermodynamic feasibility of this step is beyond question. It is

a more interesting task to examine the second step of the reduction process:

CuCl,s + 1/2H2,g = Cu,s + HCl,g (77)

Copper mono-chloride is a relatively stable compound. Although chlorides are prone to

evaporation, this one has a boiling point higher than 1600 oC, therefore its evaporation may

become significant only at high temperatures. This should be avoided if the reduced metal is not

intended to be obtained as a mirror on the wall of the reactor. This is demonstrated by Fig. 32,

showing a quartz reactor tube removed from the furnace. In an experimental attempt, the copper

chloride raw material was reduced at a temperature as high as 800 oC, when the rate of evaporation

could be high enough that the practically instantaneous homogenous reaction in the gas phase

produced more metal than the direct heterogeneous reduction of the solid sample in the quartz boat

placed in the centre of the tube. The applied resistance heating transferred heat through the tube

wall, which became the hottest surface where the reaction mostly happened. The homogeneously

reduced metal was deposited at the inner wall of the reactor tube.

Fig. 32 The copper produced by the reduction of copper chloride at high temperature.

Quartz boat with the sample and the product

Copper layer produced at the inner surface of the tube

82

However, the melting point (423 oC) of CuCl sets an even narrower limit to the temperature than

the rapidly growing vapour pressure. It may be beneficial to approach it but it must not be

surpassed, because the high specific surface of the fine crystalline material would be lost by

melting and the kinetic conditions of the heterogeneous reaction with the gas phase would be

ruined. Thus the temperature range of 25 – 423 oC can be targeted for the examination. However,

the process cannot be described by a single function of GØ(T) even in this relatively narrow

interval as the CuCl compound suffers a phase transformation at 407 oC, which has a

similar heat effect as melting. Thus below the transition temperature the thermodynamic

characteristics of the substances in the following equation (with the phases marked in the

subscripts) must be considered:

CuCl, + 1/2H2,g = Cu,s + HCl,g (78)

The standard thermodynamic data of the components in Eq. (78), referring to 298 K and

the heat capacity functions valid in the noted ranges are arranged in Table 7. The tabulated data

refer to the amounts of the components noted in reaction (78), and were derived by multiplying

the molar values of the databases by the stoichiometric factors in the reaction equation. Thus the

tabulated data refer to the amounts of the components as participating in the reaction, marked

accordingly in the first column. They can be used directly to determine the thermodynamic

characteristics of the reduction of one mole CuCl with the stoichiometric amount of hydrogen,

producing copper and hydrogen chloride.

Table 7. Thermodynamic data of the component material units in reaction (78)

Component

(Products

Reagents)

Standard enthalpy

of formation

Standard

entropy Standard heat capacity function,

𝐻298 , J/mol 𝑆298

, J/(molK) 𝐶p, J/( molK) Interval, T,K

Cu,s 0 33.137 22.635+6.27610-3 T 298-1356

HCl,g -92312 186.786 26.527+4.60210-3 T + 1.088105 T-2 298-2000

CuCl,, -137235 86.190 70.628+41.8410-3 T 298-680

1/2H2,g 0 65.270 13.640+1.63210-3 T + 0.251105 T-2 298-3000

83

The standard enthalpy change and entropy change of the reaction can be determined directly from

the tabulated data for room temperature:

𝐻298 = 𝐻298,Cu,𝑠

+ 𝐻298,HCl,𝑔 − (𝐻298,CuCl,

+ 𝐻298,1/2H2,𝑔

)= 0 - 92312 –(-137235 + 0) =

= 44924 J/mol (79)

𝑆298 = 𝑆298,Cu,𝑠

+ 𝑆298,HCl,𝑔 − (𝑆298,CuCl,

+ 𝑆298,1/2H2,𝑔

) = 33.137 + 186.786 –(86.19 + 65.27) =

= 68.492 J/(mol K) (80)

Applying the above results, it is possible to determine the standard free enthalpy change of reaction

(78) for room temperature:

𝐺298 = 𝐻298

− 298 · 𝑆298

= 44924 - 29868,492 = 24513 J/mol (81)

As this value is strongly positive, this reaction cannot be expected to proceed with the materials

in their standard states at room temperature. However, due to the positive entropy change,

increasing the temperature is beneficial. Therefore, it is worth continuing the computation and

introducing the correction based on the heat capacity functions, the standard free enthalpy change

should be determined also for higher temperatures. The standard heat capacity change function of

the reaction is expressed as below:

𝐶p = 𝐶p,Cu,𝑠

+ 𝐶p,HCl,𝑔 − (𝐶p,CuCl,

+ 𝐶p,1/2H2,𝑔

) = 22.635 + 6.27610-3 T + 26.527 +

+4.60210-3 T + 1.088105 T-2 – (70.628 + 41.8410-3 T +13.640 + 1.63210-3 T + 0.251105 T-2) =

= -0.586–32.59310-3T+0.837105T -2 , J/(mol K) (82)

A further function is derived from the above result by dividing it with the temperature:

𝐶p

𝑇 = -

0,586

𝑇- 32.59310-3 + 0.837105 T -3 , J/mol (83)

The definite integrals with running upper limits are created from the last two functions in the

narrowest temperature interval noted in the last column of Table 7.

84

∫ 𝑇

298𝐶pd𝑇 = -0.586T – 16.29710-3 T 2 – 0.837105 T -1 – (-0.586298 – 16.29710-32982 –

0.837105298-1) = 1904-0.586T-16.29710-3T2-0.837105T-1 , J/mol (84)

∫𝐶p

𝑇d𝑇

𝑇

298 = -0.586lnT – 32.59310-3T – 0.418105T-2 - (-0.586ln298-32.59310-3298 –

0.418105298-2) = 13.514–0.586lnT–32.59310-3T–0.418105T-2 , J/(mol K) (85)

Applying the above results to relationship (72), the standard free enthalpy change of reaction (78)

can be expressed as a function of the temperature:

𝐺(𝑇) = 𝐻298 + ∫ 𝐶p

d𝑇𝑇

298− 𝑇 (𝑆298

+ ∫𝐶p

𝑇d𝑇

𝑇

298) =

44924+1904-0.586T-16.29710-3T2-0.837105T-1 – T(68.492 + 13.514 – 0.586lnT – 32.59310-3 T

– 0.418105T-2) = 46827-82.592T+16.31810-3T2-0.418105T-1+0.586TlnT, J/mol (86)

This function yields the standard free enthalpy change values of the examined reaction for the

temperatures (in Kelvins) in the range until no transition of state happens (until 680 K). A good

control is the practically equal results obtained for room temperature by Eqs. (81) and (86). A

positive result for room temperature may not exclude the feasibility of the reaction, since it is not

necessary to apply standard conditions in practice. The practical requirement of feasibility for a

reaction is the lower value of the activity index than that of the equilibrium constant.

Therefore, it is indispensable to determine the equilibrium conditions, described by the equilibrium

constant for the given temperature. This is carried out by applying the relationship (73):

𝐾 = exp (−𝐺

R𝑇) = 10

(−𝐺

R𝑇 )

ln10 ≅ 10

(−𝐺

R𝑇 )

2.303 (87)

As two of the components in Reaction (78) are pure solid phases, whose activities can be taken as

unity, the equilibrium constant can be expressed with the fugacities - approximated by the partial

85

pressures at higher temperatures – of the gas components at the reagent and product sides. Thus

the value of the equilibrium constant at room temperature is:

𝐾 =

𝑝HCl𝑝o

√𝑝H2𝑝o

= 10(−

24518 8.314∗298

)

2.303 = 10-4.297 = 5.0410-5 (88a)

𝑝HCl

𝑝o = 5.0410-5 √

𝑝H2

𝑝o (88b)

This reaction can be carried out in a tube furnace, which can be fed with a practically pure

hydrogen, then the gas mixture will consist of H2 and HCl, the reagent and the product components.

As the system has a free exhaust, thus it is under atmospheric pressure (po = 1) and - besides the

equilibrium constant - the following equation can be formulated for the partial pressures:

𝑝H2

𝑝𝑜+

𝑝HCl

𝑝𝑜= 1 (89)

The total pressure of the gas mixture in the furnace tube is equivalent to the atmospheric pressure.

Thus the partial pressure of hydrogen chloride can be expressed with that of hydrogen

(𝑝HCl = 𝑝𝑜 − 𝑝H2). Rearranging the system of the two equations, leads to following equations:

1 −𝑝H2

𝑝𝑜= 5.0410−5√

𝑝H2

𝑝o (90)

1 − 2𝑝H2

𝑝𝑜+ (

𝑝H2

𝑝𝑜)2= 25.410−10 𝑝H2

𝑝𝑜 (91a)

0 = −(𝑝H2

𝑝𝑜)2+ (25.410−10 + 2)

𝑝H2

𝑝𝑜− 1 (91b)

The physically meaningful solution of the last quadratic equation gives the equilibrium partial

pressure of hydrogen normalized to the atmospheric pressure (formerly expressed in “atm” units):

86

𝑝H2

𝑝𝑜=

1

2(2 + 25.4 · 10−10 − √(2 + 25.4 · 10−10)2 − 4) = 0,9929 (92a)

or in general:

𝑝H2

𝑝𝑜=

1

2(2 + 𝐾 − √(2 + 𝐾)2 − 4) (92b)

Thus, for the examined reaction (78) to proceed even at room temperature, hydrogen should

make up almost the entire pressure (higher part than 99.3%), provided that only the reagent and the

product gases constitute the gas mixture of the reaction. To seek more feasible conditions, higher

temperatures can be substituted into the function (86), and in turn, with the obtained new standard

free enthalpy change values expression (88) yields the new equilibrium constants, with which the

relevant equilibrium hydrogen partial pressures can be determined as shown above. These values

are given in Table 8 in the temperature range extending to the transition point of the α-CuCl crystal.

Table 8 Thermodynamic characteristics of reducing one mole of α-CuCl with hydrogen

Temperature, Go Equilibrium constant Equilibrium H2 conc.

oC K J/mol (𝑝HCl/𝑝o) (√𝑝H2/𝑝o)⁄ %

25 298 24518 5.03810-5 99.3

100 373 19472 1.87510-3 95.8

200 473 13028 0.03641 82.7

300 573 6916 0.23416 61.9

400 673 1138 0.81596 41.7

407 680 744 0.8767 40.4

The approximate computed results, based on the partial pressures, demonstrate that increasing the

temperature strongly favours the feasibility of the planned reaction (78). Although the relevant

standard free enthalpy change is still positive at the limiting value, 407 oC, of the stability of the α-

CuCl, the reduction is possible at this point more than 43% hydrogen content can be assured in the

H2 + HCl gas mixture in the reactor, since the value of the activity (fugacity) index is less than that

of the equilibrium constant. However, a reagent concentration only slightly higher than the

equilibrium value can quickly drop below the critical value if the supply is slower than the rate of

the reaction. Thus it is advisable to surpass the limiting hydrogen partial pressure significantly. It

assumes the correct setting of the feeding rate of the reagent gas in a tube furnace system assuring

87

a continuous flow. The results of the above thermodynamic examination are illustrated graphically

by the plots of Fig. 33.

Fig. 33 Thermodynamic characteristics of reducing one mole of α-CuCl with hydrogen

(a – standard free enthalpy change, b – equilibrium constant, c – equilibrium hydrogen partial

pressure) as functions of the temperature.

The analytical formulae used for the computation of the marked points are also included in the

diagrams, as well as the regression functions and correlation coefficients defining the best fit curves

adjusted to the computed points. The temperature dependence of the standard free enthalpy seems

quite linear in this representation despite the rather complex polynomial function. However, the

value of the equilibrium constant is increasing steeply above ca. 500 K, which reflects the

theoretically exponential relationship. Nevertheless, the decrease of the equilibrium hydrogen

pressure becomes rather uniform in this range. The hydrogen partial pressure required for Reaction

(78) can be assured by the constant gas flow at a relatively low temperature too. However, it means

only the feasibility of the devised reaction. For a practical optimization, the reaction rate has to be

considered too, which – as to be shown later – also strongly depends on the temperature.

The temperature range of the previous computation was limited by the point of the α-β

transition of copper chloride at 407 oC. Although the reaction proved possible from a

thermodynamic point of view within this limit too, it may be useful for kinetic reasons to increase

a) b) c)

88

the temperature further. For this to examine, the previous thermodynamic computation has to be

complemented with the reaction of phase transformation:

CuCl, = CuCl, (93)

According to the general expression (72), the -CuCl starting material (reagent) can be replaced

by -CuCl, more stable at higher temperatures, if reaction (93) is formally subtracted from the

basic reaction (78) in the temperature range above 407 oC:

(94)

which combination (A – B = C) yields the reactions:

C: CuCl, + 1/2H2,g = Cu,sz + HCl,g (95)

corresponding to the state of copper chloride after the phase transition. The thermodynamic data of

reactions (94A) and (94B) can be summed in the same manner.

For the purpose of addition, the thermodynamic functions of reaction (93) has to be

determined in the same way as shown for reaction (78) above. Naturally, this is a much easier

procedure, as there are only two components to count with. At 407 oC, or 680 K, the standard

enthalpy change associated with the transition reaction (93) is the heat of transition. I has a value

of 𝐻680,() = 6067 J/mol, and the entropy change derived from it is 𝑆680,()

=6067

680 = 8.922

J/(mol K). The form of copper chloride is stable from 407 oC to its melting point at 423 oC

(696 K). The heat capacity of the transformed -CuCl is given as a constant value, 𝐶p,CuCl, =

64.685 J/(mol K), in the data base, since it only exists in a very short temperature range. This has

to be summed according to expression (94) algebraically the heat capacity function of -CuCl

given in Table 7 resulting in the heat capacity change function of the transition reaction:

𝐶p,() = 28.577 – 41.8410-3T. In the next step this is divided by the temperature to derive the

other important function: 𝐶p,()

𝑇=

28,577

𝑇− 41.8410−3. The obtained functions can be integrated

in the new temperature range, yielding the following results:

A: CuCl, + 1/2H2,g = Cu,sz + HCl,g

B: - (CuCl, = CuCl,)

89

∫ 𝑇

680𝐶p,() d𝑇 = -9757 + 28.577T – 20.9210-3T2 , J/mol, (96)

and

∫𝐶p,()

𝑇

𝑇

680d𝑇 = -157.946 + 28.577lnT – 41.8410-3T , J/(mol K) (97)

Thus the standard free enthalpy change of the transition reaction:

𝐺𝑇,() = 𝐻680,()

+ ∫ 𝑇

680𝐶p,() d𝑇 − 𝑇 (𝑆680,()

+ ∫𝐶p,()

𝑇

𝑇

680d𝑇)=

= - 3690+ 177.61T + 20.9210-3T2 – 28.577TlnT , J/mol (98)

Summing the expressions of the basic (86) and that of the transition (98) reactions yields the

standard free enthalpy change function of the overall reaction in the 680 – 696 K temperature range:

𝐺𝑇,(680−696) = 50517 – 260,203T – 4,60210-3T2 – 0,418105T-1 + 29,162TlnT, J/mol (99)

Thus Table 8 can be extended with some more results for further temperatures, which are

summarized in Table 9.

Table 9 Thermodynamic characteristics of reducing one mole of β-CuCl with hydrogen

Temperature, Go Equilibrium constant Equilibrium H2 conc.

oC K J/mol (𝑝HCl/𝑝o) (√𝑝H2/𝑝o)⁄ %

410 683 586 0.902 41.7

420 693 117 0.98 39

423 696 -21 1.004 38.2

Thus the functions describing the reduction of monovalent copper chloride have a breakpoint at

the transition temperature of 407 oC or 680 K. For the range below that point Eq. (86), above that

Eq. (99) is the valid equation for the standard free enthalpy change functions, which are

fundamental in assessing the feasibility of the reaction. In order to assure lower requirements of

hydrogen and higher rates of the reaction at the same time, it is worth approaching the melting

90

point of the raw material, which is rather low in this case. The values of the composed functions

are shown in Fig. 34.

Fig. 34 Thermodynamic characteristics of reducing one mole of α-CuCl and one mole of β-CuCl

with hydrogen (a – standard free enthalpy change, b – equilibrium constant, c – equilibrium

hydrogen partial pressure) as functions of the temperature near the transition and melting points.

It is evident that raising the temperature in the narrow range available above the transition

until the melting of -CuCl has no real thermodynamic significance. The limiting equilibrium

concentration of the reagent hydrogen gas is not reduced further significantly. Approaching the

melting point too sharply, on the other hand, may be dangerous because of the partial melting of

the reagent material. Such an intention may however be justified by sensitive kinetic

characteristics, to be examined later.

More G(T) functions obtained by a similar computational method are shown in Fig. 35

for the formation and reactions of other copper compounds besides CuCl. By comparing the

standard free enthalpy changes, it is possible to assess the relative stability and transformability of

metal compounds.

91

Fig. 35 Standard free enthalpy changes in the Cu-Cl-H system.

The reactions of G(T) functions high in the positive range of the diagram describing the

complex system in the standard state are not feasible. They can occur only under extreme

concentration conditions. Therefore, the thermal dissociation of CuCl cannot be expected, and the

92

oxidation of CuCl2 is neither likely whichever grade of copper oxide would be the product. At the

same time, it is obvious that CuO is the stable copper oxide in the relatively low temperatures range

(800 ~ 1000 K) characteristic of roasting, while at the higher (above ~ 1400 K) temperatures of

smelting the lower grade oxide, the Cu2O may dominate. The curve of the standard free enthalpy

change associated with the reaction of CuCl with H2, discussed in detail above, can be found in the

middle of Fig. 35, thus its feasibility may strongly depend on the actual concentrations of the

components. The reduction of copper oxides is characterized by much simpler thermodynamic

conditions. Melting and evaporation do not interfere with the raising of the temperature and the

characteristic standard free enthalpy curves are in the strongly negative range of the diagram.

Therefore, the thermodynamic possibility of putting the process into practice is generally

favourable and the driving force is increasing slightly with temperature.

If properly interpreted, comparing the standard free enthalpy change functions may show

the relative possibility of the reactions correctly. It is interesting to compare the G(T) curves

referring to the direct evaporation and dissociation of CuCl2. As the latter runs lower at

temperatures below 900 K, the heating of the copper dichloride may result the more stable

monochloride instead of volatilization. Although the lowering of pressure enhances volatilization.

In the presence of hydrogen, however, CuCl2 is likely to be transformed into CuCl directly, whose

reduction may happen under the conditions discussed above. Another possibility is the evaporation

of CuCl by forming the trimeric Cu3Cl3 molecules, but the thermodynamic feasibility of the direct

reduction with hydrogen is also greater. The mechanism of the reaction may however be decisively

influenced by the transport processes of the reagents and products. All these conditions have to be

taken into account in devising a practical hydrogen reduction process.

As shown by the numerical example discussed in detail above - the practical feasibility of

the reactions is more accurately assessed by the free enthalpy changes referring to the actual

conditions – which may be significantly different from those of the normal state – or by the

limiting activities (concentrations, partial pressures) of equilibrium. The equilibrium gas pressures

determined from the thermodynamic functions[24] included also in Fig. 35 are shown in Fig. 36.

The greater values of the equilibrium gas concentrations are plotted on a linear scale in the upper

half of the diagram, whereas the smaller values are shown on a logarithmic scale in the bottom half.

The relevant reactions are summarized below the diagrams. There is no plotted function for the

93

first reduction step “R2” of CuCl2, as the relevant equilibrium hydrogen pressure is approximately

zero, thus the reaction can proceed under any circumstances.

Fig. 36 The concentrations or partial pressures of the main components in the gas mixtures formed

by the reduction and the oxidation (a),or decomposition and evaporation (b) of copper compounds.

94

Reaction “R1” was examined numerically above (referring to 1 mole of the starting material). The

resulting equilibrium hydrogen concentration in the gas mixture of the reaction is significant, but

it is decreasing with temperature. Higher reagent concentration can be easily achieved, and this

reaction step can be executed. The equilibrium hydrogen pressures are even lower for the

reduction of oxides, therefore their reduction is even easier. However, increasing the temperature

seems unfavourable in their case, as the equilibrium hydrogen pressure rises. Nevertheless, this

effect does not cause difficulties, since the limiting values still remain very low. Figure 36.b shows

the partial pressures of significant gases evolved by the dissociation or evaporation of copper

compounds in the examined temperature range, applying different scales in the two halves of the

diagram. It is seen that the CuCl2 compound easily dissociates to CuCl and Cl2 as the temperature

is raised. This process may be followed by the evaporation of the chlorides. Only CuO, the higher

oxide of copper shows any tendency of dissociation, yielding Cu2O at higher temperatures.

4.5 The formation and reduction of metal oxides

The most important practical application of chemical metallurgy is in the reduction of

metal oxides, constituting a major class of ores, and the separation of impurity elements by

oxidation, which constitutes the prevalent method of fire refining of metals. Besides all that, the

metal content of sulphide ores can be extracted also by controlled oxidation. In this case, however,

the degree of oxidation may be critical, which has to be assured by the conscientious control of the

thermodynamic conditions. In case of the sulphide raw materials of high metal content the primary

objective is a complete oxidation, which is carried by the oxidising roasting of the ground and

concentrated ore in solid-gas heterogeneous system. The metal can be obtained subsequently by

reduction smelting. This step usually means carbothermic reduction carried out in a shaft

furnace. However, if the sulphide raw material contains significantly less than 50% metal even

after physical concentration, direct extraction may involve too high losses of the metal. In this case

further concentrating steps are required by pyrometallurgical methods. This is carried out usually

by a partially oxidising roast followed by a mildly reducing smelting where the converted part of

the originally sulphide accompanying materials are transferred into the molten oxide slag, and the

valuable metal can be concentrated in a separate sulphide melt, the matte. The main metal can be

extracted from the sulphide matte and more oxide slag can be formed by a strictly controlled

95

oxidation process in molten state, referred to as converting. All these procedures can be carried

out under the appropriate thermodynamic conditions, which can be assessed only by the

examination of the oxidation processes of metals and metal sulphides.

Applying the method described in Section 4.4.4, it is possible to set up the standard free

enthalpy change functions for the oxidation reactions of the elements. The oxidation of metals can

be compared by the standard free enthalpy changes of the general reactions constructed for 1 mole

of the reagent:

2𝑥Me + O2 =2

𝑦Me𝑥O𝑦 (100)

The stability of a given metal oxide is indicated by the more negative change in the free enthalpy

(released energy) accompanying its formation. As the oxidation of a pure metal usually takes place

in its condensed state and the produced metal-oxide forms a separate solid phase, the process can

be considered in normal state if the partial oxygen pressure is unity. The sections of the dashed

lines in the lower temperature range of Fig. 37 thus practically reflect the standard free enthalpy

changes of metal oxide formation reactions. This section of the quasi-linear curves can be

interpreted according to relationship (15). The intercept of the G(T) function curve with the

vertical axis corresponds to H, and the slope shows the -S value.

As the produced metal oxide is usually condensed, most often solid, and there is 1 mole

oxygen gas at the reagents’ side, the reaction implies a corresponding negative entropy change.

As the characteristics of oxide formation are always compered referring to 1 mole of the reagent

oxygen, these curves start regularly with parallel sections. This trend is broken at the boiling point

of a so far condensed component. As generally the metal – being on the left of the equation - has

the boiling point earlier, the curves become here steeper, also maintaining linearity. The slope is

proportional to the value of the stoichiometric coefficient, x, in reaction (100), i.e. the more metal

is included in the left side of the oxidation reaction. This means the conversion of more gas into

the solid oxide at temperatures beyond the boiling point. The increased slope is caused by the

multiplied value of the entropy change. This breakpoint falls in the examined practical temperature

range of Fig. 37 in the case of zinc, but its position is also influenced by the actual partial pressure

of the metal vapour.

96

Fig. 37 Thermodynamic conditions of oxide formation and stability.

According to the relationship of vapour pressure and temperature (46), the boiling point of zinc,

i.e. the temperature which causes the vapour pressure to reach the given value, decreases from the

standard 918 oC to approximately 500 oC if the pressure is only 0,01 bar. The section of the curve

beyond the breakpoint becomes steeper as the pressure is decreased, since the entropy change in

the reaction where the gas is converted into the solid oxide causes more negative change in the

entropy of the system. The entropy change of the reaction is basically determined by the volumetric

ratio of the gases on the two sides of the equation. In the case of iron oxidation, also marked in Fig.

37, no breakpoint is seen, as the boiling point of the metal lies out of the covered temperature range.

The slope of the curve belonging to lead changes in the opposite direction at the first breakpoint.

This indicates the rather unusual case when the boiling point of the oxide (PbO) is lower than that

of the metal. This implies an increase in the entropy as a result of oxidation. Naturally, the position

of the breakpoint shifts with the pressure as in the previous case.

97

As an important practical application of Fig. 37, it is useful to compare the standard free

enthalpy changes of the various oxides at a given temperature. The metal that forms a more stable

oxide, whose standard free enthalpy change function runs lower, can take away the oxygen from

a less stable metal oxide. This property serves as the basis for aluminothermy, as a practical

application. As the oxidation of aluminium shows strongly negative standard free enthalpy change,

a large number of metal oxides can be reduced if aluminium is contacted with the metal oxide to

be reduced in a fine dispersion and theoretically at any temperature. However, the kinetic

conditions of the reaction require a suitably high temperature, besides the high specific interfacial

surface which assures the efficient contact of the contiguous phases. Such heterogeneous

reactions can only take place at the interface between the phases, therefore the fine particle size

and good dispersion are fundamental conditions of aluminothermic reduction of metal oxides. As

the material is heated to a sufficiently high temperature, the molten aluminium may develop a better

contact with the surface of the metal-oxide particles. Naturally, this method is only justified

economically if the reduced metal is significantly more valuable than aluminium, which – by

oxidation – gets into the practically worthless slag. If an even stronger reducing agent is required,

the use of magnesium can be considered. The application of magnesiothermic reduction is not

restricted to the reduction of metal oxides, but valuable metals are also produced from chloride raw

materials or from intermediate products converted into the chloride form. This is the way how

titanium, a metal of unique properties and a material indispensable in space technology and

biotechnology, is produced.

Figure 37 suggests even further options for the reduction of metal oxides, which can serve

the production of technical metals of lower value. This is based on a cheaper reducing agent,

which has enabled the pyrometallurgical metal extraction to become a method of large scale

production. The affordable and readily available, although moderately efficient – reducing agent is

primarily carbon monoxide, which can be produced in situ in the metallurgical apparatus.

Carbothermic reduction is a well-known method of metal extraction from early times, and it is

used today for the production of the most common raw metal, the pig iron.

The reducing power of carbon monoxide, however has to be adjusted by controlling the

thermodynamic conditions. The reduction of the metal oxide implies the oxidation of the reagent

carbon monoxide, which has to be more stable than the metal oxide to be reduced. The stability of

the carbon dioxide by-product can be examined according to the basic reaction:

98

2CO + O2 = 2CO2 (101)

This reaction hardly ever can proceed under standard conditions, as all the components are in a

common gas phase. According to Fig. 37, unlike aluminium, carbon monoxide would not be

capable of reducing most of the metal oxides under standard conditions. However, the CO2-CO-O2

system can be diverted from the standard conditions as much as required. If only the oxygen

partial pressure is fixed at unit value, the oxidation of metals is still characterised by the standard

free enthalpy change (GØ ), but for reaction (101), a less definite free enthalpy change (G~)

depending also on the relative concentration of the two CO/CO2 carbon oxide gases will apply.

The relationship can be derived from the general expression of the free enthalpy change of a

reaction:

𝐺 = 𝐺 + 𝐑𝑇ln𝐼 (102)

where I is the activity index, which can be expressed – with good approximation - in this case with

the partial pressures. By substituting the unit partial pressure of oxygen, the following expression

is obtained:

𝐺2CO2

~ = 𝐺2CO2

Ø + 𝐑𝑇ln(𝑝CO2𝑝𝑜

)2

1 (𝑝CO𝑝𝑜

)2 = 𝐻2CO2

Ø + 𝑇 (2𝐑ln𝑝CO2

𝑝𝐶𝑂− 𝑆2CO2

Ø ) (103)

Thus in Fig. 37, the G~ function describing the oxidation of carbon monoxide at unit oxygen

partial pressure is described by an array of lines, whose slope decreases with the 𝑝CO 𝑝CO2⁄ pressure

ratio. The oxide forming properties of volatile metals may also depend on the gas composition. In

the case of zinc, also featured on Fig. 37, the free enthalpy change of reaction

2Zn + O2 = 2ZnO (104)

99

may differ from the value referring to standard conditions above the breakpoint, corresponding to

the boiling point of the metal. The partial pressure of the zinc affects the free enthalpy change of

oxidation referring to an oxygen partial pressure of unity:

𝐺2ZnO~ = 𝐺2ZnO

Ø + 𝐑𝑇ln1

1 (𝑝Zn𝑝𝑜

)2 = 𝐻2ZnO

Ø + 𝑇 (2𝐑ln1

(𝑝Zn𝑝𝑜

)2 − 𝑆2ZnO

Ø ) (105)

At a lower pressure, the section beyond the breakpoint is steeper, as suggested by Eq. (104). At the

same time, the breakpoint is also shifted to lower temperatures because of the lowering of the

boiling point. The higher position of the G~ curve makes zinc oxide easier to be reduced, although

the metal can be obtained as a vapour in this case.

It can be seen on Fig. 37 that the reducing power of the CO-CO2 gas mixture can be strongly

influenced by the ratio of the partial pressures of the two carbon oxide gases. By decreasing the

concentration of CO2 to a suitable level, i.e. increasing the 𝑝CO 𝑝CO2⁄ partial pressure ratio and the

temperature, carbon monoxide can be made capable of reducing theoretically any metal oxide.

In order to enhance the reduction with carbon monoxide, reducing the relative concentration

of CO2, the Boudouard reaction can be applied:

CO2 + C = 2CO (106)

Fig. 38 illustrates that temperature has a fundamental role affecting the relative concentrations of

CO and CO2 in the system described by Eq. (106).

Fig. 38 The Boudouard equilibrium as a function of the temperature at constant pressure.

100

In processes operated at the standard pressure, the Boudouard reaction assures the dominance of

CO in the vicinity of 1000 oC in a CO+CO2 gas mixture, if the appropriate amount of porous

carbon is also available. Reducing the pressure may even enhance the production of CO, according

to the Le Chatelier principle. Carbon dioxide, formed by the reduction of the metal oxide is

converted back to carbon monoxide by the involved action of hot carbon exhibiting an appropriate

specific surface area. However, carbon monoxide is originally produced from the primary

burning of carbon resulting directly in carbon dioxide, since with the abundant oxygen supply in

the hot blast introduced at the combustion zone, the

C + O2 = CO2 (107)

reaction proceeds by any means, but as the gas leaves the oxidation zone the Boudouard reaction

assures the conversion to carbon monoxide. As the flue gas is driven out, the burning of the coke

is necessary for the reproduction of the reducing gases.

The curves in Fig. 37 can be interpreted as describing the “relative oxygen potentials”

derived from the equilibrium fugacity of oxygen participating in the given reaction. According to

the definition:

O2

= 𝐺O2− 𝐺O2

∅ = R𝑇ln𝑓O2 (108)

where the fugacity of oxygen (𝑓O2) may be substituted by its relative partial pressure (𝑝O2

𝑝o⁄ ) in

the case of the high temperature processes. The „” notation here refers to the deviation from the

standard value in the expression of the chemical potential – as in Eq. (30) - for oxygen. The value

of the equilibrium oxygen fugacity can be deduced from the formula (34) of the equilibrium

constant referring to the oxidation reaction (100). The equilibrium constant can be determined in

this case from the standard free enthalpy change of formation of the oxide 2

𝑦Me𝑥O𝑦):

R𝑇ln𝐾 = R𝑇ln𝑎MexOy

2𝑦

𝑎Me2x ∙𝑓O2

= −𝐺2

yMexOy

(109)

101

From where the relative oxygen potential of the given oxidation reaction can be expressed with the

equilibrium oxygen fugacity – practically the relative partial pressure:

R𝑇ln𝑝O2

𝑝𝑜≅ R𝑇ln𝑓O2

= 𝐺2yMexOy

+ R𝑇ln𝑎MexOy

2y

𝑎Me2x

=

= 𝐻2

yMexOy

+ 𝑇 (Rln𝑎MexOy

2y

𝑎Me2x − 𝑆2

yMexOy

) (110)

It can be seen, that for the oxidation reaction implying the separate pure phases of the metal and

metal oxide, the relative oxygen potential is equivalent to the standard free enthalpy change.

Therefore, the relative stability of metal oxides can also be determined in the way that oxygen is

stronger bound in the oxidation reaction of a metal where the relative oxygen potential –the

developing equilibrium oxygen pressure - is lower. This metal can reduce another oxide whose

formation is related to a higher relative oxygen potential, if the two system co-exist. The general

expression (110) is simpler if the stoichiometric parameters are of unity values (x = 1 and y = 1),

when the metal is divalent in its oxide. This case is very significant because the reduction of the

higher oxides of the transition metals happens in subsequent steps, whose final and critical one is

the reduction of the most stable MeO form:

MeO + CO = Me + CO2 (111)

This reaction can proceed if the oxidation of CO has lower equilibrium oxygen pressure than that

of the oxidation of zinc. It can be reworded as the oxidation of CO has a lower relative equilibrium

oxygen potential than that of the oxidation of zinc. For the oxidation of zinc above the breakpoints

of the curve in Fig. 37 - corresponding to the boiling points of zinc - the activity of the metal cannot

be considered generally of unity, since its stable form is the vapour. Therefore, the curve of the

relative equilibrium oxygen potential continues in different sections corresponding to the marked

vapour pressures, as described by the following modified expression:

102

R𝑇ln𝑝O2

𝑝𝑜≅ R𝑇ln𝑓O2

= 𝐻2MeO + 𝑇 (2Rln

𝑎MeO

𝑎Me− 𝑆2MeO

) (112)

The relative equilibrium oxygen potential, referring to the oxidation of the reducing agent (CO)

can be expressed in a similar simple form:

R𝑇ln𝑝O2

𝑝𝑜≅ R𝑇ln𝑓O2

= 𝐻2CO2

+ 𝑇 (2Rln𝑝CO2

𝑝CO− 𝑆2CO2

) (113)

It should be noted that the expression of the relative equilibrium oxygen potential is equivalent to

the free enthalpy change referring to unit value of the relative partial oxygen pressure (𝐺~) in the

same oxide forming reaction. It is seen for example in the comparison of Eqs. (103) and (113).

According to the equilibrium relative oxygen potential functions appearing in Fig. 37, the

reduction of PbO does not require any excess CO in the gas mixture, and FeO can be reduced with

a relatively slight excess of CO. Even the stronger bound ZnO can also be reduced by increasing

the CO/CO2 pressure ratio and the temperature. However, this is practically feasible above the

boiling point of zinc, therefore, the obtained metal is not separated as a melt, but it can leave the

furnace in the vapour state. The use of the shaft furnaces – similar to the blast furnace applied in

producing pig iron – is the most advantageous choice for reduction. The gas phase containing CO

and H2 can execute the reduction in the shaft as it is efficiently contacted with the charge consisting

of porous particles and pieces. This is the best arrangement not only for the heat transfer, but also

for the reaction mechanism. However, in the case of zinc, the produced metal vapour also travels

upward in the shaft, where the temperature must be kept high enough to prevent re-oxidation.

Zinc vapour leaving the hot furnace can be condensed by intensive cooling, when re-oxidation is

avoided by the kinetic conditions.

The thermodynamic conditions of oxide formation and reduction are shown in a more

elaborate way in the Ellingham-diagram of Fig. 39.

103

Fig. 39 Standard free enthalpy changes and equilibrium relative oxygen potentials of oxide

formation.

104

The equilibrium relative oxygen potential lines of CO oxidation can be drawn from point “C” at

the left side to the points corresponding to the marked CO/CO2 partial pressure ratios on the scale

at the right side. The diagram also shows the relative oxygen potential lines belonging to the

reaction:

2H2 + O2 = 2 H2O (114)

of hydrogen oxidation. The lines referring to the relevant formula:

R𝑇ln𝑝O2

𝑝𝑜≅ R𝑇ln𝑓O2

= 𝐻2H2O − 𝑇(2Rln

𝑝H2

𝑝H2O+ 𝑆2H2O

) (115)

can be drawn from point “H” at the left side to the point s corresponding to the marked H2/H2O

partial pressure ratios on the scale at the right side. Reduction with hydrogen is possible in

practice. It can assume an important role not only in the case of producing pure metals from their

chlorides – as described in the numerical example above – but also in the case of carbothermic

metal extraction in a shaft furnace. Hydrogen is formed by the reaction of water vapour with carbon

at high temperature in this system, and due to its fast pore diffusion, it can enhance the reduction

of oxide ores and concentrates. There is a third scale at the right side of Fig. 39, which gives the

approximate value of the equilibrium relative oxygen potential where the straight line drawn from

point “O” at the left through the selected point of the curve belonging to the given oxidation

reaction intersects it.

It can be seen also from the position of the curves that a very high ratio of CO/CO2 would

be required for the reduction of Al2O3 in the temperature range below 2000 oC, still compatible

with the refractory materials. This would imply an excessive coal consumption. On top of that,

aluminium would react excessively with coke to form carbides. Therefore, instead of the

pyrometallurgical extraction based on carbothermic reduction, aluminium is produced by a

cathodic reduction of the oxide. The alkaline earths form even more stable oxides. Their reduction

requires even more energy, but they are still in demand. Magnesium is used in large quantities for

example in alloying aluminium. However, the common pyrometallurgical methods are not suitable

for its extraction. This is why MgO is used as an outstanding refractory material in high-

105

temperature equipment. Utilizing, however, the relatively low boiling point and the high volatility

of the metal, and combining the high temperature reduction with vacuum, magnesium vapour can

be obtained from its oxide by silicothermic reduction. Still, the more often applied method for its

extraction is the cathodic reduction from the chloride melt.

The oxidation of metal sulphides is the basic pyrometallurgical processing step of sulphide

ores/concentrates, but it may be also applied as a preparatory roasting step in hydrometallurgical

metal extraction. The thermodynamic characteristics of the processes can be examined as discussed

in the case metal oxidation. Figure 40 shows the standard free enthalpy changes for the oxidation

of the most important sulphides.

Fig. 40 Thermodynamic characteristics of metal sulphide oxidation [19].

106

As seen from the diagrams on Figs. 35 and 40, the oxidation of metals, and especially of the metal

sulphides are exothermic processes, liberating significant amounts of heat. Thus, generally, there

is no need for a specific heating for the pyrometallurgical processes based on such reactions (the

roasting of sulphide raw materials, the converting of sulphide melts and the selective oxidation of

impurities in a metal melt). The reduction of metal oxides, on the other hand, is based on

endothermic reactions. The heat consumption of the reducing processes is usually covered by the

combustion heat of carbon.

The unfavourable aspect of oxidizing sulphide materials is the generation of sulphur

dioxide containing gases. Therefore, not only the precipitation of flue dust but also the capture

of sulphur dioxide must be assured in parallel with such metallurgical operations. The most

convenient solution, if the SO2 concentration is sufficiently high, is the production of sulphuric

acid as a metallurgical by-product. Because of the incomplete gas collection and the generation of

some dilute gases at certain technological steps, hydrometallurgical extracting technologies are

gaining significance, as they exclude the danger of air pollution.

4.6 Dissolution and precipitation in aqueous media

Hydrometallurgical technologies represent alternative ways of metal extraction, ever

increasing in significance. Applying them means not only the exclusion of air pollution, but also

the advantageous possibility to process low grade and complex raw materials and to obtain a high

purity metal directly. This is based on the relatively good solubility of metals and metal compounds

in aqueous media. The technologies applying dilute sulphuric acid, the most common, readily

available solvent, which demands only common structural materials, have spread widely. However,

hydrochloric acid and neutral ammoniacal solutions can also be applied in special cases, as well

as alkaline media in the case of extracting amphoteric metals. The metal content of oxide raw

materials can be leached by relatively simple methods. However, the solubility of metal sulphides

is much worse, therefore, some special techniques may also be required. Sulphides may be

transformed into oxides by a preliminary oxidizing roast after the usual physical concentration, or

they can be partially converted into sulphates too for assuring the acid balance in the

hydrometallurgical cycle. New processes have also been developed capable of leaching sulphides

in acidic or complexing media under oxidising conditions. Dissolution of the valuable metal is

107

always made possible by the equilibria evolved in the solution phase, which can be characterised

generally by the Pourbaix diagrams. They show the stability conditions of the formed ions or

compounds according to the acidity of the solution and the redox potential.

For metals to dissolve, they basically have to lose their valence electrons to form positive

ions (cations). It may happen in a common corrosion-type process in relation to the decomposition

of water:

Me + 𝑢H2O = Me𝑢+ +𝑢

2H2 + 𝑢OH− (116)

If the medium is acidic, the concentration of the hydrogen ions capable of oxidising the metal is

higher and the dissolution is enhanced. The practically important transition metals can form

hydrated ions of various oxidation numbers. In this case, oxygen dissolved in the aqueous

medium may further oxidise the primarily formed cations:

Me𝑢+ +𝑤−𝑢

2O2 + (𝑤 − 𝑢)H2O = Mew+ + (𝑤 − 𝑢)OH− (117)

However, especially the cations of higher oxidation number are capable of forming stable

hydroxides, which may result in hydrolysis and precipitation:

Me𝑤+ + 𝑤OH− = Me(OH)𝑤 (118)

As the ionic product of water is constant, hydrolysis is accompanied by its dissociation:

𝑤H2O = 𝑤H+ + 𝑤OH− (119)

Summing the last two reaction gives the resultant process of hydrolysis:

Me𝑤+ + 𝑤H2O = Me(OH)𝑤 + 𝑤H+ (120)

Thus increasing pH forms the basis of hydrolysis. However, as seen in Eq. (120), it is accompanied

by the production of acid in a stoichiometric amount corresponding to that of the hydrolysing

108

metal. Therefore, hydrolysis may become continuous only if the produced acid is neutralised.

Hydrolysis may be disadvantageous as much as it disrupts the stability of the solution. At the same

time, it is an important tool in hydrometallurgy as a method for the removal of dissolved impurity

ions. As hydrolysis occurs at different pH values depending on the solubility of the metal

hydroxides, the reaction is suitable for the selective removal of the dissolved cations. The

equilibrium concentrations of the cations can be expressed as functions of the pH on the basis of

the dissolution and solubility data of the metal hydroxides [25Sillén, L.G.: Stability Cconstants of Metal-

ion Complexes, Spec. Publ. No.17, The Chemical Soc. London, 1964] and the reaction (118). The

corresponding equilibrium constant can be written as follows:

exp (−𝐺Me(OH)𝑤

R𝑇) = 𝐾Me(OH)𝑤

≅𝑎Me𝑤+·𝑎OH−

𝑤

1 (121)

where the activity of the metal hydroxide precipitated in crystalline form can be considered as

unity. The results are summarized in Fig. 41.

Fig. 41 The equilibrium activities of dissolved ions as functions of the pH.

109

The constructed logarithmic curves indicate the decreasing solubility of the metal ions as the pH

value is increased. Iron, which is readily soluble in acids, is the most frequent accompanying

element in the raw materials of the most valuable metals. Hydrolysis may be suitable for the

purification of solutions of the metals most often extracted by hydrometallurgical methods (Zn,

Mn, Cu, Co…) based on the common sulphuric acid leaching, but for this purpose, the ions of the

dissolved iron should be brought to the highest Fe(III) oxidation state. The reason is seen in Fig.

41, as orders of magnitude lower residual iron concentration can be reached in this way even at

a relatively low pH. This condition assures the dissolved state of the main metal, while iron can be

precipitated as Fe(OH)3. Aluminium – and other metal ions of three or higher valences - can be

removed by a similarly good efficiency. However, precipitation is reversed in the cases of a few

amphoteric metals (like aluminium, zinc or tin) if the pH is further increased allowing the re-

dissolution of the metal in a hydroxo-complex anionic form:

Me(OH)w + (𝑥 − w)OH− = [Me(OH)x]|w−x|sgn(w−𝑥) (122)

The central core of the hydroxo-complex ion is the metal cation, which is surrounded by the

strongly bound hydroxyl ion ligands. The coordination number x depends on the concentration

of the ligand ions in the solution and on the quality of the metal. The resulting charge is the

difference of the charges of the metal cation and the ligand anions. The stable tetrahedral (x = 4)

and octahedral (x = 6) complex structures arise the most often. However, in media containing the

complexing ions in lower concentrations, some ligand positions may be occupied still by water

molecules, thus the resulting charge of the metal-complex ions may vary with the composition of

the medium.

Metals dissolved in hydrochloric acid media may form chloro-complex ions in a similar

way [26Kékesi, T., Isshiki, M.: Anion Exchange Behavior of Copper and Some Metallic Impurities in HCl Solutions.

MATER. TRANS. JIM, 35, 6 (1994), 406-413]. Chloride ions have a strongly complexing nature, and

form complex ions with a large number of transition metal ions, whose variable resulting charge

depends on the chloride ion (~hydrochloric acid) concentration:

Me𝜈+ + (𝑥 − 𝜈)Cl− = [Me(Cl)𝑥]|𝜈−𝑥|sgn(𝜈−𝑥) (123)

110

This property can be utilized for the separation of metals dissolved in hydrochloric acid media

and for the high purification of the solutions by anion-exchange method [27Kékesi, T., Isshiki, M.:

Anion Exchange for the Ultra-High Purification of Transition Metals, ERZMETALL, 56, 2, (2003) 59-67.]

Metals can be present in aqueous media in their ionic forms. As the metallic character is

indicated by the tendency releasing the valence electrons, the metal cations are formed in the

presence of suitable oxidizing agents, which attract the dipolar water molecules causing hydration.

Dissolution of metals in aqueous media is usually based on the oxidising effect of the hydrogen

ions:

Me + 𝑢H+ = Me𝑢+ +𝑢

2H2 (124)

The presence of other oxidising agents, which are more active to take over the outer electrons of

the metal atom, will enhance dissolution, which is a result finally of the interaction between the

formed ions and the water molecules. Oxidation is necessary also in the case of amphoteric metals,

which can dissolve also in alkaline media,

Me + 𝑤H2O + (𝑥 − 𝑤)OH− = [Me(OH)𝑥]|𝑤−𝑥|sgn(𝑤−𝑥) +

𝑤

2H2 (125)

Also metal oxides, the main raw materials of hydrometallurgy, need to be reacted with the medium,

but they are already in an oxidised form, so they can dissolve in acids or – in the case of amphoteric

oxides – in alkalis too:

Me𝑝O𝑝𝑢

2+ 𝑝𝑢H+ = 𝑝Meu+ +

𝑝𝑢

2H2O (126)

Me𝑝O𝑝𝑤

2+

𝑝𝑤

2H2O + (𝑥 − 𝑝𝑤)OH− = 𝑝[Me(OH)𝑥]

|𝑤−𝑥|sgn(𝑤−𝑥) (127)

The processes of dissolution, complex formation and precipitation, introduced above proceed

towards the equilibria in the solution. The possibilities are dictated here also by the thermodynamic

properties, which can be defined usually by the consideration of solubility and complex stability

constants. Leaching of sulphides require more complex reactions. This method is mostly applied

for the sulphide copper ores. The necessary condition for the dissolution of metal sulphides is the

111

oxidation of sulphur bound in the compound by oxygen, but with the contribution of some other –

usually Fe(III) sulphate – reagent:

Me𝑢S + Fe2(SO4)3 = Me𝑢SO4 + 2FeSO4 + S (128a)

2S + 3O2 + 2H2O = 2H2SO4 (128b)

2FeSO4 +1

2O2 + H2SO4 = Fe2(SO4)3 + H2O (128c)

These oxidation reactions are catalysed by enzymes produced by autotrophic bacteria, which

provides ground for bio-hydrometallurgy. However, the reaction can be enhanced also by the

application of high oxygen pressure. The latter solution is efficient and provides more concentrated

and cleaner solutions, but the autoclave operation requires more complex technical conditions. If

the metal can form complex ions, dissolution may be assisted also by complexing agents.

4.7 Electrode potentials and redox equilibria

Dissolution of metals is possible by forming the ionic state. Ionization means the complete

or partial detachment of the valence electrons, resulting in the formation of metal cations with

positive charge. In the case of the transition metals, more than one oxidation state can be stabilized

depending on the oxidizing power of the system. The electron transfer can be brought about also

by an electric power supply which is connected to the metal immersed in the solution. The

interface between the immersed metal and the solution of its dissolved ions is the electrode, and

the changes taking place here by the transfer of electrons, leading to an equilibrium constitute the

electrode process. The electrode potential arising at the metal electrode results from the electron

transfer illustrated in Fig. 42.

Fig. 42 Processes causing the electrode potential at the metal electrode.

112

If the resultant electrode process is the deposition of a metal, electrons are transferred from the

metallic material of the electrode through the interface to the cations arriving here, which are thus

reduced and deposited at the electrode surface. With this, the electrode acquires a positive charge.

At the same time, the opposite reaction also occurs, as metal ions can leave the electrode and by

hydration they enter the solution while electrons are left behind at the electrode. This may result in

the accumulation of free electrons. The sign and value of the charge resulting at the electrode

depends on the relative strengths of the two opposite processes. If the deposition of the cations is

dominant, a more positive potential relative to the solution will develop at the electrode, which

will limit the flux of positive ions to the electrode surface. The opposite process – although

originally weaker - is simultaneous, but the developed positive potential will enhance it. This way,

a dynamic equilibrium is established in which the two opposite processes are of equal rate.

In case the dissolution of the metal – producing cations - is the predominant process by its

nature, the potential of the metal electrode is shifted in the negative direction, which will in turn

limit the process of dissolution, the generation and the departure of positive ions. A negative

potential, on the other hand will enhance the originally weaker process of metal deposition from

the positive cations, and the dynamic equilibrium is established at a potential more negative in

relation with the solution. The spontaneous process arises from a chemical driving force which is

held in equilibrium with the developing electrode potential. The thermodynamic driving force of

the dominant process, arising from the free enthalpy change, provides the energy required to move

the particles of ionic charge through the electrostatic field at the interface corresponding to the

electrode potential (E):

𝐺 = 𝐅𝐸 (129)

where the charge carried by one mole ions is expressed with the Faraday constant (F 96500 As)

as F, and E is the potential difference between the electrode surface and the solution. Thus the

dominant process related to this free enthalpy change is by any means negative but the electrode

potential may be of different signs, depending on the direction of the process. Expression (129)

renders opposite signs for the cases of deposition and dissolution dominance. In the case of the

reduction of cations:

113

Me+ + e− = Me (130)

the electrode isolated from an external circuit will become more positive, therefore the negative

sign applies in expression (129). If the opposite process is dominant and cations are formed

spontaneously, the isolated electrode attains negative charge, and the positive sign applies to the

relationship (129). Thus expression (129) can be evolved both for the reduction of cations and the

oxidation of the metal atoms separately:

𝐺red = 𝐺red + R𝑇ln

𝑎Me

𝑎Me+= −F𝐸Me+/Me (131a)

𝐺ox = 𝐺ox + R𝑇ln

𝑎Me+

𝑎Me= F𝐸Me+/Me (131b)

As the free enthalpy changes of the two opposite processes are of equal absolute value with

opposite signs, the same expression can be derived for the electrode potential from both directions:

𝐸Me+/Me = 𝐸Me+/Me +

R𝑇

Fln

𝑎Me+

𝑎Me (132a)

which may be written for 298 K as:

𝐸Me+/Me = 𝐸Me+/Me + {

0,0591

lg

𝑎Me+

𝑎Me}298K

(132b)

where 𝐸Me+/Me is the standard electrode potential, which arises from the standard free enthalpy

change terms in expressions (131), although it differs from the 𝐺red (−F)⁄ or the 𝐺ox

(F)⁄

value by a constant of reference. The electrode potentials are not expressed in an absolute sense,

but – based on measurability – they can be used as relative to the value of the standard hydrogen

electrode. The potential of a metal electrode thus corresponds to the voltage of such a cell where

one of the electrode is this metal in its own solution and the other is the standard hydrogen

electrode. The latter gives the potential evolved on a platinum wire immersed in a solution of

114

hydrogen ions of 1 mol/dm3 concentration in the presence of hydrogen gas bubbled at atmospheric

pressure. This arrangement is illustrated by Fig. 43.

Fig. 43 The sketch and the processes of a cell consisting of a metal electrode and a standard

hydrogen electrode.

The equal potentials of the two electrolyte solutions and - in case of a finite resultant current – the

balance of the anions is assured by a conducting salt-bridge connection. The electrode potential of

the metal can be measured by a voltage gauge of high resistance between the examined metal and

the Pt outlet of the reference electrode. The dissolution of the metal electrode is the potential

determining process in the outlined system. This can cause a higher accumulation of electrons at

the metal than the electron density at the standard hydrogen electrode, thereby resulting in a more

negative potential. However, it depends on the kind of the metal. The standard electrode potentials

of the practically utilized elements, shown in Fig. 44 as functions of the atomic numbers, can be

interpreted accordingly.

115

Fig. 44 The standard electrode potentials of the more common elements in the characteristic

oxidation states as functions of the atomic number.

The different electrode potentials of more than one oxidation states can be seen on the curves of

Fig. 44 in the cases of each common transition metal (Ti, V, Cr, Mn, Fe, Co and Cu) at the same

given atomic number. It can be seen that elements at the beginning of the periods can form cations

easily. It is in correlation with the great reactivity of the alkali, alkaline earth elements and those

of the transition elements that are less saturated with electrons. Ionized noble metals and non-

metallic elements would rather gain electrons, therefore they are characterised by more positive

electrode potentials than that of hydrogen. The strong tendency of reactive metals to form cations

by losing – and leaving behind - electrons is manifested in more negative electrode potentials, while

the characteristics of less reactive metals, retaining their electrons or neutralizing the cations, are

indicated by their more positive electrode potentials. The transfer of electrons means simultaneous

reduction and oxidation processes, thus the electrode potentials are redox potentials as all the

simple electrode processes can be interpreted by the redox reaction:

Ox+ + e- Red (133)

116

where “Ox” and “Red” are the oxidised and the reduced forms of the matter taking part in the

electrode process. The general reaction (133) may express the formation or the neutralisation of

the metal ions:

Me+ + e- Me, (134)

or the transformation of multi-valent (w+ and u+) ions between their valence states (when is the

number of the change in the ionic charge):

Mew+ + ze- Meu+ (135)

Measurement of redox potentials related to the transformation of cations of different oxidation

states is also possible by the potential obtained from an inert (usually Pt) electrode. Therefore, the

formula (132) can be generalised, leading to the Nernst-equation:

𝐸Ox/Red = 𝐸Ox/Red +

𝐑𝑇

𝐅ln

𝑎Ox

𝑎Red= 𝐸Ox/Red

+ {0,0591

lg

𝑎Ox

𝑎Red}298 K

(136)

In the case of a metal electrode of first order corresponding to the cathodic metal deposition or

anodic dissolution by the reaction (134), the cations represent the oxidised and the neutral atoms

the reduced forms, thus:

𝐸Me+/Me = 𝐸Me+/Me +

𝐑𝑇

𝐅ln

𝑎Me+

1 (137)

In this case the activity of the reduced form is unity, as it refers to the pure crystalline state.

The electrode potential of hydrogen, referring to the process:

H+ + 𝑒− =1

2H2 (138)

depends on the pressure of the gas and the acid concentration in the solution:

𝐸H+/

1

2H2

= 0 +𝐑𝑇

𝐅ln

𝑎H+

√𝑝H2

≅ 0 +𝐑𝑇

𝐅ln

𝑐H+

√𝑝H2

= 0 +𝐑𝑇

0,4343𝐅lg

𝑐H+

√𝑝H2

(139)

117

As the hydrogen electrode is the general reference, its standard electrode potential is zero by

definition 𝐸H+/

12H2

= 0. Therefore, only the difference related to the deviation from the standard

state appears in relationship (139). Substituting the ion activity in dilute solutions by the mol/dm3

concentration, usually used in electrochemistry, the electrode potential of hydrogen can be

expressed as a function of the pH:

𝐸H+/

1

2H2

= 0 −𝐑𝑇

0,4343𝐅(pH + log√𝑝H2

) = {0,0591pH + 0,0295lg𝑝H2}𝑇=298𝐾

(140)

In aqueous solutions, the possible evolution of oxygen at higher potentials may also gain

significance. The electrode potential of oxygen arises from the deposition or generation of

hydroxyl ions:

4OH- -4e- O2 + 2H2O (141)

However, the dissociation equilibrium of water re-supplies the deposited hydroxyl ions while

hydrogen ions are generated too:

4H2O = 4OH- + 4H+ (142)

Reactions (141) and (142) are linked process steps, and they result in:

2H2O – 4e- = O2 + 4H+ (143)

Thus, according to the overall reaction, the electrode potential of oxygen is:

𝐸O2/2H2O = 𝐸O2/2H2O +

𝐑𝑇

4𝐅ln

𝑐H+4 𝑝O2

1= 1,21+

𝐑𝑇

𝐅ln𝑐

H+ +𝐑𝑇

4𝐅ln𝑝O2

(144)

Where 1.21 V is the standard potential of the oxygen electrode with 1 mol/dm3 hydrogen ion

concentration in the solution. Which means that also the electrode potential of oxygen depends on

the pH value, i.e. the acid concentration of the solution, even so, it is in the same way as in the

case of the hydrogen electrode potential:

118

𝐸O2/2H2O = 1.21− {0.0591pH − 0.0148lg𝑝O2}298 K

(145)

The same result can be obtained from the partial reaction (141) but in that case a different standard

state and the pertaining (0.4 V) standard potential would apply according to the 1 mol/dm3

concentration of the hydroxyl ions. The hydrogen and the oxygen electrodes are gas electrodes,

whose potential also depends on the pressure of the given gas. The potentials of these two gas

electrodes determine the stability range of water. This is shown in Fig. 45. The electrode potential

of hydrogen – according to relationship (140) – is described by curve (a) and that referring to

oxygen - according to relationship (145) – is denoted by curve (b) in a graphical form, referring to

atmospheric pressures.

Fig. 45 The stability of water and the electrode potentials of hydrogen a and of oxygen b as

functions of the pH. (25 oC, 𝑝H2𝑝o⁄ = 𝑝O2

𝑝o⁄ = 1). [28Pourbaix, M, Zoubov, N, Van Muylder, J.: Atlas

d’Équilibres Électrochimiques, Gauthier-Villars, Paris, 1963.]

The thermodynamic stability area of water is bounded by the two parallel lines denoting the

evolution of (a) hydrogen and (b) of oxygen. Reactions in aqueous solutions have to be carried out

within this range in order to avoid the evolution of hydrogen or oxygen. According to equation

(137), the potential of a metal electrode - of the first order – depends on the concentration of its

own ions. This is shown schematically by Fig. 46.

119

Fig. 46 Schematic of the electrode potentials of different metal and gas electrodes as functions of

the ion concentration at a constant temperature.

In a solution of multiple cations, the cathodic deposition of that one is preferred whose electrode

process has the most positive electrode potential. The more positive potential indicates the greater

number of electrons taken up by the cations in equilibrium. In the case of the anodic direction, on

the other hand, the process of more negative electrode potential will be preferred. In this way, it

is possible to deposit and dissolve metals selectively by electrolysis. According to equation (136),

the equilibrium electrode potentials can be depicted by straight lines referring to the logarithm of

the relevant oxidised ion concentration at a constant temperature. The slope is inversely

proportional to the change in the charge number of the ions determining the electrode process.

The electrode potential of metals – similarly to that of hydrogen – is increasing relatively

slowly with the logarithm of their ionic concentrations. The change in the opposite direction may

be even more significant, as the ion supply by diffusion may not maintain the concentration during

the fast deposition of the metal ions at the cathode. This may result in a strong decrease of the

electrode potential. According to Fick’s law, the flux of the electro-active ions at the cathode

surface of unit area:

d𝑛Me+

Ad𝑡= −D grad𝑎Me+ ≅ −D

d𝑎Me+

d𝑥≅ −D

𝑎Me+,s − 𝑎Me+,b

(146)

120

where n is the molar amount of the ions arriving at the surface of “A” area, and D is the actual

diffusion coefficient. The direction of the diffusion transport is normal to the effective surface of a

sufficiently large electrode, therefore it may be considered as unidirectional. The concentration

profile, also normal to the electrode surface, which maintains the diffusion, can be linearized

yielding the diffusion layer thickness. Therefore, the ion concentration is lower at the surface of

the cathode than in the bulk solution (𝑎Me+,s < 𝑎Me+,b), and the potential of the cathode will be

consequently lower, which explains the phenomenon of diffusion polarization and overpotential.

The electric current density (j) corresponds to the rate of diffusion and thus to the change in the

concentration at the electrode surface:

𝑗 = Fd𝑛Me+

Ad𝑡≅ −FD

𝑎Me+,f − 𝑎Me+,b

(147)

which – in the case of the surface concentration of the metal ions at the cathode dropping to zero –

may result in the cathodic limiting current (jl) of maximum value.

𝑗l ≅ uFD 𝑐Me+,b

(148)

Its value is proportional to the ion concentration in the dilute bulk solution if the thickness of the

diffusion layer, i.e. the stirring intensity is constant. Further polarizing the cathode beyond

approaching the limiting current may not practically increase the current, and the polarization can

result in infinite negative potentials too. The overpotential of the metal cathode arising from

diffusion type polarization (ηdiff) results from the equilibrium expression (137) referring to the

decreasing concentration at the electrode:

𝜂diff = 𝐸Me+/Me

=R𝑇

uFln

𝑎Me+,s

𝑎Me−

R𝑇

Fln

𝑎Me+,b

𝑎Me =

R𝑇

uFln

𝑎Me+,f

𝑎Me+,b

(149)

There is a change in the concentration at the anode surface in the opposite direction, which may

also meet a limiting condition. In the case of electrorefining with a soluble anode, the opposite

processes of the two electrodes are illustrated by Fig. 47.

121

Fig. 47 Schematic of the electrode processes developing at the soluble anode and the metal

cathode (ja, jc, a, c – anodic and cathodic current densities and diffusion layers).

Applying the correlations of concentration changes and electric currents (147-149), the relationship

of cathodic diffusion overpotential and the electric current density can be expressed:

𝐸Me+/Me =𝐑𝑇

𝐅ln (1 −

𝑗

𝑗l) (150)

Therefore, the cathodic metal deposition cannot be carried out with any current density. As the

limiting current density is approached, the cathode potential can shift so much in the negative

direction that is not only harmful to the electric energy consumption but deposition of some

impurities of negative electrode potentials may also occur. On a strongly polarized cathode, loaded

with a largely negative potential, an intensive evolution of hydrogen may also arise, even when

copper – the metal with a positive standard electrode potential – means the main electrode process.

However, it does not happen at mildly negative electrode potentials as the deposition of the

hydrogen ions may also require significant overpotentials.

There is another different type of overpotential component, which is independent from the

concentration changes in the solution. The relevant theoretical background was founded by the

investigations of the Hungarian scientist, Tibor Erdey-Grúz [29Erdey-Grúz, T: Elektródfolyamatok

kinetikája, Akadémiai kiadó, Budapest, 1969]. It is stated that the overpotential imparted to the electrode

decreases the activation energy of the step related to the charge transfer (or to the deposition

and the formation of the ions). The resulting current density depends on the activation

overpotential according to the Erdey-Grúz-Buttler-Volmer equation:

122

𝑗 = |𝑗ox| − |𝑗red| = 𝑗𝑜 {exp (αoxz𝐅𝜂act

𝐑𝑇) − exp (−

αredz𝐅𝜂act

𝐑𝑇)} (151)

where jox, jred, αox, és αred are the partial current densities of the oxidation and reduction directions,

the transfer coefficients and jo is the exchange current density, which is found at equilibrium of

equal absolute magnitude in both directions. The cathodic partial current density in the reduction

direction (jred) is negative, which results from the negative potential of the electrode relative to the

equilibrium. The transfer coefficients – together with the charge number (z) of the electroactive

ions – determine how much the electrode potential modifies the energy requirement of the partial

processes. As the two opposite processes (oxidation and reduction) are running at the same time,

their rate is equal in equilibrium. Polarizing the potential in the positive direction results in a

dominance of the anodic process, and a negative shift produces a net cathodic process. This is

illustrated by Fig. 48, where the electrode functions as an anode in the positive segment and as a

cathode in the negative one.

Fig. 48 The partial current densities developing at the electrode as functions of the activation

overpotential.

The resultant of the oxidation and reduction partial current densities – corresponding to the

exponential tags of eq. (151) and shown as dashes lines – is the actual current, whose curve

intersects the origin. The anodic component of eq. (151) can be neglected at high cathodic

overpotentials, yielding the relationship corresponding to the empirical Tafel-equation [29] for the

absolute value of the current density:

123

|𝜂act. cath.| = −𝐑𝑇

αz𝐅ln (

|𝑗red|

𝑗𝑜) =

𝐑𝑇

2,303αz𝐅lg𝑗𝑜 +

𝐑𝑇

2,303αz𝐅ln|𝑗| = 𝐚 + 𝐛 lg|𝑗| (152)

where a és b are constants characteristic of the type of the material and the effect of the current

density. One of the most important practical aspect is the hindered deposition of hydrogen at

different metals. The higher hydrogen overpotential makes it possible to deposit metals of negative

electrode potential from aqueous – even from slightly acidic – solutions. The characteristic Tafel-

plots are shown in Fig. 49.

Fig. 49 The overpotential of hydrogen deposited at different metal cathodes.[28]

124

Hydrogen can be deposited for example at the surface of zinc only at a significant overpotential,

which allows the deposition of this metal from slightly acidic solutions despite its relatively

strongly negative (-0.76 V) standard electrode potential, given in Fig. 46. However, in the case of

copper, the overpotential of hydrogen is much lower therefore hydrogen deposition may occur at

the copper cathode if the concentration of the copper ions is strongly decreased by applying high

current densities.

According to the equilibria in Fig. 45, metal ions may also react with water if the pH

value is increased. Figure 50 shows the E-pH (Pourbaix-type) diagrams describing the equilibria

of various redox and hydrolytic reactions which may happen in aqueous media considering the

possible oxidation states of the copper ions and the possibly produced oxides. The standard

electrode potential of copper is shown by horizontal lines and the vertical lines indicate the

equilibria of hydrolysis at the noted logarithmic values of the ion concentrations. The slanting lines

refer to the complex redox and hydrolysis reactions.

Fig. 50 The equilibrium E-pH diagram of Cu in meta-stable (a) and stable (b) states. [28]

125

The electrode potentials described by horizontal lines are independent of the pH value. The vertical

lines correspond to the pH values resulting from the equilibrium constants of purely hydrolysis

processes at the given ion concentrations. The slanting lines indicate the equilibrium conditions

when redox and hydrolysis partial reactions are combined. The electrode potential of the redox

reaction involving also the decomposition water:

qMe + rH2O = MeqOr + 2rH+ + 2re− (153a)

MeqOr + sH2O = MeqOr+s + 2sH+ + 2se− (153b)

can be expressed by applying the fundamental thermodynamic relationships of Eqs. (32) and (129):

𝐸MeqOr/Me = 𝐸MeqOr/Me +

𝐑𝑇

2r𝐅

𝑎MeqOr

𝑎Me+ 2r

𝐑𝑇

2r𝐅ln𝑎H+ = 𝐸MeqOr/Me

+ {0,0591pH}298 K (154a)

𝐸MeqOr+s/MeqOr= 𝐸MeqOr+s/MeqOr

+𝐑𝑇

2r𝐅

𝑎MeqOr

𝑎Me+ 2r

𝐑𝑇

2r𝐅ln𝑎H+ =

= 𝐸MeqOr+s/MeqOr

+ {0,0591pH}298 K (154b)

As the activities of the solid components can be considered as unity, it is dependent only of the pH

value at a given temperature. The equilibrium conditions indicated by the straight lines separate

the stability areas of the different possible forms of the examined metal. As the line is crossed by

the conditions, the relevant reaction occurs in the direction yielding the preferred product indicated

in the neighbouring territory. The predominance area diagrams – known as Pourbaix-diagrams

– show the directions of the reactions in the given territories in function of the redox potential of

the system and the pH value, as parameters, indicating the products, which may be the metal or its

ions and compounds. If the aqueous solution also contains complexing agents, more species may

be formed and the area of hydrolysis – resulting in precipitation – can be reduced. This is

exemplified by the stabilization of tin ions in chloride solutions even at higher pH, which is

illustrated by Fig. 51.

126

Fig. 51 The equilibrium E-pH diagram of tin in the Sn-H2O (a) and Sn-H2O-Cl (aCl− = 1) (b)

systems [30G.H. Kelsall and F.P. Gudyanga: Thermodinamics of Sn-S-Cl-H2O system at 298 K, Journal of

Electroanalytical Chemistry and Interfacial Electroche. Vol. 280,1990. 267-282.]

The formation of complex ions influences also the electrode potential of the metal. The redox

potential determined by two adjacent oxidation states of the metal:

Mew+ + (w − u)𝑒− = Meu+ (155)

𝐸Mew+/Meu+ = 𝐸Mew+/Meu+ +

𝐑𝑇

(w−u)𝐅

𝑎Mew+

𝑎Meu+ (156)

The activities/concentrations of the electroactive species are modified by the complex formation:

Me𝜈+ + 𝑥Cl− = [MeCl𝑥]|𝜈−𝑥|sgn(𝜈−𝑥) (157)

The effective concentration of the aquo ions (Me𝜈+) is reduced by the amount of the formed

complex ions:

𝑐Me𝜈+ = 𝑐Me − 𝑐[MeCl𝑥]|𝜈−𝑥|sgn(𝜈−𝑥) = 𝑐Me − 𝛽𝜈,𝑥(𝑎Cl−)𝑎Me𝜈+ (158)

The redox potential may increase or decrease, depending on whether the aquo ion of the higher

(w+) or the lower (u+) adjacent oxidation states tends to form complex ions. Continuing to examine

the example of tin, Fig. 52 shows the effect of the chloride ion concentration on the electrode

a) b)

127

potential in the Sn-Sn(II)-Sn(IV) system. The stability areas of the chloro-complex ions

([MeCl𝑥]|𝜈−𝑥|sgn(𝜈−𝑥)) also appear besides those of the metallic tin and the aquo ions (Sn2+, Sn4+)

in the E-pCl- diagram. Increasing the chloride ion concentration, i.e. decreasing the pCl- value,

the Sn(II)/Sn electrode potential becomes significantly lower than in a neutral solution. This is

indicated by the lower slanting line. Thus the cathodic deposition of tin and other metals that form

chloride complexes (Zn, Fe, Cu, Co) may be more difficult from HCl solutions than from other

acidic media. However, by the formation of the chloride complexes a higher stability of the

solution can be achieved, and the higher purity of the metal obtained from chloride media after

melting the cathode may be some more important aspects. The co-deposition of hydrogen at the

cathode is a common difficulty when acid solutions are applied. The chloride ion concentration can

be increased while the concentration of the hydrogen ions – dangerous to the cathodic current

efficiency – is kept low by the addition of alkali chlorides. However, the residual electrolyte

entrapped by the rough structure of the cathode metal - usually obtained from chloride

electrolytes – will not contaminate the melted metal if HCl is used. The evolution of H2 can be

suppressed by higher metal concentrations in cases of low hydrogen overpotentials (Fig. 49).

Fig. 52 Dominant ionic forms in the Sn-H2O-Cl system.

128

Aqueous solutions play important roles in recovering and refining metals. However, there are some

metals of practical importance (e.g. Al, Mg), whose stable cations are so difficult to reduce - i.e.

their electrode potentials are strongly negative –that they cannot be deposited on a metal cathode

from aqueous media in competition with the evolution of hydrogen. Such highly reactive metals

can be reduced only from their ions formed in high temperature molten salts. The salt may

contain more stable – usually alkali metal – cations.

5 The kinetics of metallurgical reactions

A thermodynamically possible chemical reaction can only be utilized in practice if the

transformation of the reagents occurs suitable speed, i.e. the equilibrium state of a closed system

would be approached in a short time. There are practical cases when the kinetic properties of the

reactions do not allow reaching the thermodynamically expected composition. Such a case is

represented by the off-gas leaving the shaft furnace in a carbothermic reduction. According to the

equilibrium conditions of Fig. 38, carbon monoxide could have only a negligible concentration in

the blast furnace gas of 200 – 300 oC temperature. Towards the equilibrium, reaction (106) should

cause the decomposition of CO in the fast rising gas of decreasing temperature. However, lower

temperature decreases the rate of this reaction too and the equilibrium is not approached quickly.

The reaction rate is also reduced by the consumption of the reactants.

Temperature has an outstandingly important role in determining the productivity and

the economy of the metallurgical processes, as it has a commonly known effect on the rates of

chemical reactions, but - according to Eq. (43) - it also affects the equilibrium constant, and it

controls the states of the materials. It may justify the development and – in many cases – the

dominance of pyrometallurgical technologies applying high temperatures for the extraction and the

purification of metals. Hydrometallurgical technologies based on the reactions of dissolved ions in

aqueous media can be applied for the same purposes and are quickly spreading, where the

temperature of the solution may also have strong effects. In both types of metallurgical procedures,

the concentrations of the reactant and the products are not only determined by the main reaction,

but the state of the system can be influenced by external means. Thus the separation of the

product(s) in a different phase may result in favourable conditions for the completion of the

129

reaction. The processes of metal extraction are most often based on reactions of substances in

different phases. Such is the reaction of a solid matter with a gas (roasting and reducing smelting),

or the reactions of a liquid phase with solid materials and gases (oxidation smelting) and the

reactions between immiscible liquid phases (melt refining). Further, the reactions of solid materials

with aqueous solutions (leaching, precipitation) or the electrode processes are of the same kind. In

such cases, the main reactions take place at the interfacial surfaces separating the phases, and the

rate of the overall process may depend on the velocity of the reaction or the speed of transport

carrying the reactants and the products to or from this surface. Thus the overall velocity of

processes may often be controlled also by the rate of diffusion, transporting the substances. In these

cases, forced convection, beside higher temperature, may efficiently enhance the process.

The role of kinetics is well demonstrated by the example of aluminium oxidation. The

corrosion resistance of this metal is well known, as well as the thermodynamic driving force of its

oxidation, shown in Fig. 39. The contradiction is resolved by the compact and stable oxide layer

formed, which prevents the access of oxygen to the interfacial surface of the metal. Therefore, this

oxidation reaction is not slowed down by approaching the equilibrium condition. It is usual that

diffusion controls the processes resulting in the transformation, extraction or refining of metals.

5.1 Determination of the rate constant

An important “constant” was also figured in the chapter on thermodynamics, which

determined the equilibrium composition of the reaction mixture. However, that was not an absolute

constant, being dependent on the temperature of a given reaction. Also in reaction kinetics, there

is a constant, indicating - at the given concentrations - the velocity of reactions, which also strongly

depends on the temperature. Expanding and transforming Eq. (26), reactions can be generally

expressed by different forms of equations as follows:

1A1 + ⋯+ 𝑛A𝑛 = 𝑛+1A𝑛+1 + ⋯+ 𝑚A𝑚 (159a)

∑ 𝑖A𝑖 = ∑ 𝑖A𝑖𝑚𝑛+1

𝑛1 (159b)

∑ 𝑖A𝑖 = 0,𝑖 (159c)

130

where i is the stoichiometric coefficient of a component (Ai). In general, the reaction rate

(velocity) is given by the amount of a component taking part in the reaction in unit volume and

unit time [31Panchekov, G.M., Lebedev, V.P.: Chemical kinetics and catalysis, MIR Publishers, Moscow, 1976].

Thus it can be defined as the rate of concentration change (−d𝑐A𝑖/d𝑡). It is sufficient to examine

the concentration change for only one reactant or product also in the case of a reaction of multiple

components, as the values referring to different components are interrelated through the ratios of

the stoichiometric coefficients in Eq. (159). The reaction rate expressed in this way for a given

component can be normalized if it is divided by the relevant stoichiometric coefficient (−

d𝑐A𝑖𝑖

d𝑡).

Thus an equivalent value can be expressed by any of the reaction components.

The rate of the reaction depends on the frequency the reagent particles collide. As the

number of reacting particles is proportional to the amount of material available in the volume, i.e.

to the reaction space, the reaction rate (W) must be proportional to the concentration of the

reagents:

𝑊 = −𝑑𝑐𝐴𝑖

𝑑𝑡= 𝑘𝑐A1

r1 𝑐A2

r2 𝑐A𝑛

r𝑛 = 𝑘 ∏ 𝑐A𝑖

r𝑖𝑛1 (160)

where “k” is the temperature dependent rate constant of the reaction, and 𝑐A𝑖

r𝑖 is the concentration

expression of the reactants with ri in the exponent as the order referring to the relevant substance.

The rate constant k yields the reaction rate when the concentrations of the reactants are of unity. If

the reaction takes place in one elemental step, the orders referring to the reactants are equivalent

to the relevant stoichiometric coefficients (ri = i). In this case the resultant order of the reaction (r)

is the sum of the coefficients, i.e. the number of the molecules (particles) producing the reaction,

which is termed as the “molecularity” of the reaction. The chemical equation, however, usually

expresses the material balance or the overall process, which may be composed of multiple steps

hindered at different levels. Therefore, the order referring to a specific reagent may differ from its

stoichiometric coefficient in the overall process, and may be expressed by fractional numbers too.

In this case, the order of the reaction cannot be predicted, rather it can be assessed only by

investigations. For concentrations that are changing in time, an average reaction rate can also be

expressed referring to the examined interval:

131

�̅� = −𝑐𝐴𝑖

𝑡=

𝑐A𝑖,𝑜− 𝑐A𝑖

𝑡𝑜− 𝑡= k𝑐A̅1

r1 𝑐A̅2

r2 𝑐A̅𝑛

r𝑛 = k∏ 𝑐A̅𝑖

r𝑖𝑛1 (161)

All chemical reactions are theoretically reversible, but in many cases one of the directions

is so dominant that the reverse process can be practically neglected. In such a kinetically

irreversible process, at least one of the reagents practically disappears from the reaction space.

Reactions are usually driven towards irreversibility when one of the products leaves the system by

converted into a separate phase (for example by precipitation from a dissolved state, or by gas

evolution). In other cases, the reverse process is enhanced by the accumulation of the products,

while the examined process is slowed down by the consumption of the reactants. Finally, the rates

of the two opposite process become equal and the system reaches equilibrium. Determination of

the equilibrium may be important for devising the procedure based on the process, or the

characterising of the reaction. It is worth examining the method referring to a first order quasi-

irreversible reaction. Such a reaction is the spontaneous decomposition or transformation of a

substance:

A1 = ∑ 𝑖A𝑖𝑚2 (162)

or such a reaction – commonly found also in practice - where the other reagent is available at

constant quantity for the examined reactant. Thus the number of particles transformed in unit time

can be proportional to the number of not yet transformed particles. [31] If the volume of the system

is practically constant within the confines of the equipment, the amount of the material can be

referred to unit volume, thus the number of particles will change proportionally to their

concentration. Assuming that the original concentration (co) is decreased by x during a time of t,

the amount transformed in unit time is:

−d(𝑐𝑜 − 𝑥) = k(𝑐𝑜 − 𝑥)d𝑡 (163a)

−d𝑐 = k𝑐d𝑡 (163b)

d𝑥

d𝑡= k(𝑐𝑜 − 𝑥) (164a)

d𝑐

d𝑡= k𝑐 (164b)

132

where c = co – x is the actual value of the concentration at time t. According to the expression, the

rate at which the actual concentration changes is proportional to the remaining concentration. The

specificity is expressed by k, which is the rate constant of the reaction. Separating the variables and

integrating this relationship yields the following forms:

−ln(𝑐𝑜 − 𝑥) = k𝑡 + C (165a)

−ln𝑐 = k𝑡 + C (165b)

The boundary condition of x = 0 at the initial state (t=0) or the substitution of c = ci at time ti can

give the value of the integral constant (C = - lnco, or C = -kt1 –lnc1). Thus k can be expressed by

rearrangement:

k =1

𝑡ln

𝑐𝑜

𝑐𝑜−𝑥 =

1

𝑡ln

𝑐𝑜

𝑐 (166)

The rate constant can also be determined independently from the initial concentration. In this case

Eq. (165b) has to be evaluated for two consecutive times (t1 and t2) and concentrations (c1 and c2):

k =1

(𝑡2−𝑡1)ln

𝑐1

𝑐2 (167)

Accordingly, the rate constant of a first order reaction (e.g. dissociation) can be determined if the

concentration of the substance is known as a function of time. It requires experimental work,

sampling and analysis. By applying finite differences instead of the differential expressions in the

rate equation (164b), the (approximate) value of the rate constant can be determined, yielding the

following expression for the monomolecular reaction of dissociation:

k̅ = −1

(𝑡)𝑐

𝑐̅ (168)

where 𝑐̅ is the average value of the concentration, whose value changes with c in a time interval

of t. The application of formulae (166), (167) and (168) leads to approximately the same result.

The dimension of the rate constant is the reciprocal of time, 1/s for a reaction of first order.

133

By eliminating the logarithm from the analytically obtained (166) expression, the exponential

functions of the concentration change and the actual concentration can be obtained:

𝑥 = 𝑐𝑜(1 − e−k𝑡) (169a)

𝑐 = 𝑐𝑜 e−k𝑡 (169b)

The concentration of the substance transformed or remaining from the reactant during the examined

first order reaction can be given by the exponential “kinetic plots” of Fig. 53. The concentrations

of the transformed and the remaining amounts are equivalent (x = c) at the intersection of the two

plots, where the amount of the reactant has decreased to just half of its initial value. Thus from the

equivalence of expressions (169a) and (169b), the „half-life” can be determined: 𝑡1/2 =ln2

𝑘

Fig. 53 The concentration of the transformed (x) and the remaining (c) substance in a first order

reaction as functions of time.

Thus it is possible to determine the amounts of the material transformed and still remaining in the

original form at any time. This may be an important practical indicator, which can be used for

devising the operation of the reactor and the technological process.

In the case of more reagents, the expression of the rate constant with the time of the

reaction and the amounts of the transformed materials may become a rather complicated

mathematical task. Reactions involving more than two reactants are however rare and usually

134

significantly slower, since the probability of more particles to meet simultaneously is little. In the

simplest case of this kind, the second order quasi-irreversible bi-molecular reaction of two

reactants (A1 and A2) may be written as follows:

A1 + A2 = A3 + A4 (170)

In this process of simple stoichiometry, x portions of both substances are transformed in unit

volume. The kinetic relationships can be derived in the same way as described in detail for the first

order reaction, but now the rate of the reaction is determined by the amounts of both reactants

available in unit volume of the reaction space.

d𝑥

d𝑡= k(𝑐A1,𝑜 − 𝑥)(𝑐A2,𝑜 − 𝑥) (171)

The rate constant can be expressed after separating the variables and applying the 1

a−bln |

a−𝑥

b−𝑥| + C

mathematical solution for the integral of the d𝑥

(a−𝑥)(b−𝑥) type expression:

k =1

𝑡

1

(𝑐A1,𝑜−𝑐A2,𝑜)ln

𝑐A2,𝑜(𝑐A1,𝑜−𝑥)

𝑐A1,𝑜(𝑐A2,𝑜−𝑥) (172)

where cA,o and cB,o are the initial concentrations of the two reactants. Whereas in the case of the

first order reaction the dimension of the rate constant was the reciprocal of time, here it is the

reciprocal of time and concentration.

If the reaction is reversible in the kinetic sense, the change observed in the system is a

result of two opposite processes. As a simple example, the reaction which is mono-molecular in

both directions can be noted as follows:

A1 k1⃗⃗ ⃗⃗

k2⃖⃗ ⃗⃗⃗

A2 (173)

Applying the principles and notations as before, the resultant velocity of transforming the reactant

can be expressed as the difference referring to the two opposite directions:

135

−d(𝑐A1,𝑜−𝑥)

d𝑡=

d𝑥

d𝑡 = k1(𝑐A1,𝑜 − 𝑥) − k2(𝑐A2,𝑜 + 𝑥) (174)

which can be rearranged as:

d𝑥

d𝑡= (k1 + k2) (

k1𝑐A1,𝑜−k2𝑐A2,𝑜

k1+k2− 𝑥) (175)

After separating the variables and integrating the obtained expression of d𝑥

(a−𝑥) type according to the

−ln|a − 𝑥| mathematical rule within the definite limits of t=0, x=0 and t=t és x= x, the final

expression can be obtained for the rate constants:

k1 + k2 =1

𝑡ln

k1𝑐A1,𝑜−k2𝑐A2,𝑜

k1+k2k1𝑐A1,𝑜−k2𝑐A2,𝑜

k1+k2 − 𝑥

(176)

The rate of the forward reaction is continually decreasing and that of the reverse reaction is

increasing until the equilibrium state is reached. The rates of the opposite reactions are equal at

equilibrium; thus the resultant rate is zero, and by the maximum amount of the transformed

substance in unit volume (xe), Eq. (174) may be rewritten as follows:

0 = k1(𝑐A1,𝑜 − 𝑥𝑒) − k2(𝑐A2,𝑜 + 𝑥𝑒) (177)

The ratio of the two rate constants of opposite directions gives ratio of the concentrations in

equilibrium, i.e. the equilibrium constant:

k1

k2=

𝑐A2,𝑜+𝑥𝑒

𝑐A1,𝑜−𝑥𝑒= K (178a)

or k2 can also be expressed:

k2 = k1𝑐A1,𝑜−𝑥𝑒

𝑐A2,𝑜+𝑥𝑒 (178b)

As a further option, dividing the right side of expression (176) by the second rate constant, the

equilibrium constant can be substituted:

136

k1 + k2 =1

𝑡ln

K𝑐A1,𝑜−𝑐A2,𝑜

K+1K𝑐A1,𝑜−𝑐A2,𝑜

K+1 − 𝑥

(179)

Finally, by resolving the simultaneous equations of (176) and (178b), both rate constants can be

determined numerically. For the case when only the starting material is present initially

(𝑐A2,𝑜 = 0), the following result is obtained for the rate constant k1:

k1 =𝑥𝑒

𝑐A1,𝑜

1

𝑡ln

𝑥𝑒

𝑥𝑒 − 𝑥 (180)

which can be substituted back into expression (178b) to yield k2.

In the case of a kinetically reversible second order reaction, the above principles can be

applied in the same way. The rate of the net process also results from the difference of the two

opposite reactions:

A1 + A2k1⃗⃗ ⃗⃗

k2⃖⃗ ⃗⃗⃗

A3 + A4 (181)

However, the mathematical solution would be very complicated in this system. As an illustration,

it is worth considering only the case when equal amounts of both reactants (𝑐A1,𝑜 = 𝑐A2,𝑜) are

present in unit volume and that of the products is zero (𝑐A3,𝑜 = 𝑐A4,𝑜 = 0) [31]. Thus the resultant

rate of the reaction:

−d(𝑐A𝑖,𝑜

−𝑥)

d𝑡= k1(𝑐A𝑖,𝑜

− 𝑥)2− k2𝑥

2 (182)

and after rearrangement:

−d𝑥

d𝑡= (k1 − k2) [𝑥2 − 2

k1𝑐A𝑖,𝑜

k1−k2𝑥 +

k1𝑐A𝑖,𝑜2

k1−k2] (183)

differential equation is obtained.

137

Considering the integrated form of this relationship and the expression of equilibrium conditions

as simultaneous equations, the specific values of the opposite rate constants can theoretically be

determined also in this case, however it is a rather complicated mathematical task, therefore it is

not expanded here.

Because of the multiple reagents and the consideration of reversibility, the system has

become hard to be treated mathematically in the above specially simplified cases. It would become

even more complicated if the variety of the stoichiometric coefficients in the general equation

(159) of reactions would make the order of the reaction a complex function too. Even more, due to

the also possible multi-step mechanism, the reaction order relevant to certain components would

be difficult to determine and would result a fractional number in many cases.

5.2 The temperature dependence of the reaction rate

The velocity of chemical reactions depends on the temperature strongly in most cases. In

order to characterize this dependence, the temperature coefficient of the reaction can be used,

which indicates the ratio of the rate constant referring to the actual and the increased temperature,

where the temperature increment is usually 10 Kelvins.

q10 = (k𝑇2

k𝑇1

)

10

𝑇2−𝑇1=

k𝑇+10

k𝑇 (𝑇2 > 𝑇1) (184)

According to wide scale experience, the value of q10 is approximately 2 ~ 3 in chemical processes

significant in for example biology. [31] Thus, increasing the temperature by 100 Kelvins may result

in an increase of the rate of the chemical reaction by (2 ~ 3)10, i.e. 1000 ~ 59000. After

logarithmizing Eq. (184), the change in the reaction rate can be expressed:

lgk𝑇2

k𝑇1

= (𝑇2 − 𝑇1)lgq10̅̅ ̅̅ ̅

10 (185)

where �̅� is the mean temperature coefficient referring to the T1 ~ T2 range. This method offers

only an approximation for the effect of temperature on the basis of the rates of the reaction observed

at two temperatures.

138

The dependence of the reaction rate on the temperature can also be derived theoretically

from the van’t Hoff expression of Eq. (43). Substituting the relationship (178a) of the equilibrium

constant expressed by the opposite rate constants, the following expressions are obtained:

d ln(k1k2

)

d𝑇=

𝐻

𝐑𝑇2=

𝐸1−𝐸2

𝐑𝑇2 (186a)

d lnk1

d𝑇−

d lnk2

d𝑇=

𝐸1

𝐑𝑇2−

𝐸2

𝐑𝑇2 (186b)

where E1 and E2 are quantities of energy dimensions referring to the two directions of the reaction.

Hence for a given reaction, the following relationship is obtained:

d lnk

d𝑇=

𝐸

𝐑𝑇2 (187)

The form useful in practice is obtained by integration:

lnk = −𝐸

𝐑𝑇+ ln𝐶 (188)

It is useful to indicate the constant of integration in a logarithmic form, because a convenient

relationship can be derived for the dependence of the rate constant on temperature after

changing to an exponential expression:

k = 𝐶exp (−𝐸

𝐑𝑇) (189)

It can be interpreted principally on the basis of the activation theory. The reaction requires the

collision of the reacting particles. However, not all of the collisions may be successful because the

energy of particles is distributed statistically and only the collision of “activated” particles –

possessing a certain minimum energy - will result in reaction. The rate of reaction will be

determined by the number of the activated particles.

139

The active state of the specific molecules, particles stands only for a short time (~ 10-13 s at room

temperature and ~10-14 s at 1600 oC) [32Biswas, A.K., Bashforth, G.R.: The physical chemistry of metallurgical

processes, Chapman & Hall, London, 1962.]. Therefore, it is not the life of the active state that determines

the rate of the reactions enfolding on a much longer time scale. However, the substances are in

equilibrium with the activated particles at all the temperatures and pressures. The rate of reactions

is actually determined by this distribution. Even before the evolution of the statistical

thermodynamic model of the material micro-systems, much experience had proved the principal

relationship of the reaction rate and the temperature. This was recognised by van’t Hoff and not

long afterwards at the end of the 19th Century, it was interpreted by Swante Arrhenius, the well-

known Swedish chemist. Accordingly, the rate constant (k) of any reaction can be expressed as a

function of the temperature as follows:

k = Pexp (−𝐸act

𝐑𝑇) (190)

where P is the pre-exponential constant characteristic of the reaction, carrying the dimension of

the rate constant, R is the universal gas constant, T is the thermodynamic temperature and Eakt is

the activation energy that is required to raise the energy of one mole of the reactants from the

average to the active level. The pre-exponential constant can be considered as the total collision

frequency of the particles, referred to as the “frequency factor” and the exponential expression

indicates the probability of a collision to cause reaction. The shape of the equation relates to the

Maxwell-Boltzmann distribution function, yielding such an exponential expression for the number

of particles having higher energies than a certain level. The Arrhenius equation is widely accepted

since its introduction, as most of the experimental results have verified it. This expression fails to

describe the relationship between the velocity and the temperature only in the cases when the

reaction mechanism is very complex.

The logarithmic form of the Arrhenius equation corresponds to expression (188), if the

frequency factor and the activation energy are indicated. Correspondingly, it is practical to plot the

logarithm of the rate constant (lnk) as a function of the reciprocal of the thermodynamic

temperature (1/T) to obtain a linear relationship, as shown in Fig. 54.

140

Fig. 54 The Arrhenius plot, showing the logarithm of the rate constant as a function of the

reciprocal temperature.

In order to establish the Arrhenius plot, the characteristic velocity of the reaction has to be

determined experimentally for a few set temperatures. It requires the determination of kinetic

curves of the type shown in Fig. 53 by the analysis of samples taken during the execution of the

reaction. Knowing the stoichiometric relationships expressed by equation (159) of the reaction, it

is sufficing to determine the concentrations of a well analysed component referring to different

times of the reaction carried out at certain temperatures. The kinetic curve of the suitable x = f(t),

or ci = f(t) type can be fitted to the points of the diagram by regression giving the best fit. This

serves to determine the rate constant referring to the given temperature. The experiment and the

plotting of the kinetic curve – and determining the rate constant from it – should be repeated to

obtain enough number of points (lnk – 1/T paired values) so as the Arrhenius line can be determined

by a linear regression of proper correlation. It usually requires a minimum of three

points/temperatures, i.e. three experimental runs. As shown in Fig. 54, it is possible to read the

slope of the constructed Arrhenius line, which is proportional to the activation energy of the

examined process.

141

The value of the activation energy indicates the characteristics of the process. By the difference of

the logarithm of the exponential expression (190) referring to two temperatures (Ta és Tb), the

approximate activation energy can also be determined directly from only two experiments:

ln𝑘b

𝑘a=

𝐸akt

R(

1

𝑇a−

1

𝑇b) (191)

However, due to the compensation of experimental error, the method based on the Arrhenius line

fitted by regression to more points is more accurate.

If the aim is specifically to determine the activation energy, it is not even required to express

the rate constants, as executing the reaction at the examined temperatures under identical

conditions of concentrations, the ratio of the characteristic velocities corresponds to that of the

rate constants:

𝑊a

𝑊b=

ka ∏ 𝑐A𝑖

𝑟𝑖𝑛1

kb ∏ 𝑐A𝑖

𝑟𝑖𝑛1

=ka

kb (192)

Substituting it into Eq. (191), yields the activation energy directly:

𝐸akt =R ln

𝑊b𝑊a

1

𝑇a−

1

𝑇b

(193)

If the experiment can be carried out under identical concentration conditions at more

temperatures, or the concentrations of the reactants are practically constant, the Arrhenius line

can be constructed by directly plotting the logarithms of the reaction rates versus the reciprocals

of the thermodynamic temperatures.

If the lnk - 1/T relationship does not show a good correlation for the linear regression and

the fitted curve obtained from the experiments sags at the lower temperatures, the dominant

mechanism of the reaction may change. It may be possible that the process implies a second order

homogeneous reaction at high temperatures, but at the lower temperature range, it may proceed

characteristically by a first order heterogeneous mechanism at the surface of the reactor wall or of

142

some other solid particles also present. In this case, diffusion, carrying the reactants and the

products to and from the interfacial surface, may become more significant. A good example for it

is given by the dissociation of nitrogen monoxide, where N2 and O2 are formed by the reaction of

two NO molecules. [31] The wall of the reactor vessel often plays a dominant role in establishing a

heterogeneous catalytic process. The two mechanisms are well distinguished if the obtained points

are divided into two separate groups showing different tendencies. The Arrhenius lines of different

slopes indicate different mechanisms. In the former example, the homogeneous range of high

activation energy is followed at a further section of the 1/T axis by a heterogeneous section of lower

activation energy and less slope of the Arrhenius line. Knowing the reaction mechanism is

important for the optimization of processes and for the development of procedures as it may decide

what aspect of the technology should be changed to accelerate the reaction. Also the value of the

activation energy in itself is a good indication of the rate controlling step of the process. At a

high range, definitely surpassing ~100 kJ/mol value, increasing the temperature – favouring the

chemical reaction may be efficient to achieve higher productivities. In the opposite case, the

convective enhancement of the material transport may lead to the desired effect.

5.3 Experimental examination of the reaction rate and activation energy

The hydrogen reduction of copper mono-chloride, numerically examined in Chapter 4.4.5,

has given an instructive example from the thermodynamic point of view. However, this

heterogeneous reaction is worth examining also from a kinetic aspect, implying some further

challenges. According to the thermodynamic computation, the equilibrium constant of the reaction:

2CuCl,s + H2,g = 2Cu,s + 2HCl,g (194)

is increasing with temperature significantly. The thermodynamic feasibility of the devised

reduction is provided by a gas mixture of higher hydrogen concentration than the equilibrium value

indicated in diagrams 33.c and 34.c. This is readily assured by a continuous gas stream, and closely

approaching the relatively low melting point did not seem thermodynamically justified. However,

the velocity of the reaction can be significantly increased by a slight change in the temperature. As

the heterogeneous reduction process is technically feasible at the high specific surface area of the

143

powdery material, the melting point of -CuCl at 696 K (423 oC) restricts the execution of the

reaction to relatively low temperatures. Therefore, it is advisable to carry out kinetic investigations

in the vicinity of the limiting temperature. For this purpose, a standard laboratory tube furnace can

be applied to advantage. The sample to be reduced should be loaded in a quartz boat placed in the

central section of approximately even temperature, as shown in Fig. 55. The reagent hydrogen gas

is continuously streamed through a preheating loop to the reactor tube.

Fig. 55 Schematic of the apparatus used for the execution of the hydrogen reduction.

The easiest way to follow the progress of the reaction is to measure the amount of hydrogen

chloride generated. The HCl component can be efficiently absorbed by introducing the off-gas into

a vessel containing a relatively large volume of vigorously stirred water, and the produced amount

can be determined by analysing the acid concentration in the periodically taken samples and the

actual volumes of the samples and the absorbent solution. Any incidentally escaped hydrogen

chloride can also be trapped and determined in the gas washer flasks applied at the outlet.

As applied in the example experiment, the CuCl sample of 25 g mass evenly packed into

the quartz boat of ~ 10 cm length and the 5 dm3/min hydrogen flow rate, the off-gas consists

dominantly of H2 and some HCl which is negligible from the aspect of the conditions of the

144

reaction.[24] The degree of reduction (α) can be expressed by the ratio of chlorine removed and the

total chlorine content in the CuCl starting material:

𝛼 =𝑛Cl

𝑛Cl=

𝑛HCl

𝑚𝑜𝑐Cl (195)

where 𝑛Cl is the actually removed amount of chlorine, equivalent to the amount of generated

hydrogen chloride gas dissolved in the absorbent water (𝑛HCl) and mo is the mass of the CuCl

sample, whose stoichiometric chlorine concentration is 𝑐Cl.

The experimental runs were carried out at three temperatures in the 681 – 691 K range,

approaching the melting point by 5 kelvins. Figure 56 shows that the rate of the reaction changes

considerably even in this narrow range.

Fig. 56. The kinetic curves of the hydrogen reduction of CuCl at different temperatures.[24]

145

The kinetic curves obtained at different temperatures can be compared by the characteristic slopes,

which can be determined as the inflexion tangents. The relatively wide central portions of the

kinetic curves shown in Fig. 56 are quasi-linear, i.re. the order may become close to zero, which

indicates the kinetic conditions of the heterogeneous reaction becoming constant. The initial

segment of the curves shows a rapidly changing slope because of the temperature setting. The

physical state of the sample still changes for a significant further period while the increasing

amount of the evolved hydrogen chloride develops the even gas penetrability in the mass of the

powder. At the final section, the decrease in the amount of the active CuCl causes the flattening of

the curve.

At the highest examined temperature, the points obtained from the parallel experiments are

independently plotted, but for the lower set temperatures, only the average values are graphically

represented. The slope defined at 681 Kelvin (~ 10 %/h) is increased by 40 % when the temperature

is increased to 691 K. The observed conversion rates can be used also for the determination of the

activation energy of the process. As the conditions of concentrations and physical circumstances

were constant at the examined characteristic segments at all the examined temperatures, according

to Eq. (192), the slope of the inflexion tangent can be considered as a virtual rate constant, if the

Arrhenius relationship is to be used for the determination of the activation energy:

k̃ = {d

d𝑡}inflex

= {1

𝑛Cl

𝑛Cl

d𝑡}inflex

(196)

In the case of the CuCl material, the removed and the total amounts of chlorine (𝑛Cl,𝑛Cl) are

equivalent to the reduced and the total amounts of copper (𝑛Cu,𝑛Cu). Thus the virtual rate

constants of the reduction, corresponding to the characteristic velocities at the examined

temperatures can be determined. Their logarithms are plotted as a function of the reciprocal

temperature as the points of Fig. 57. The linear regression by the least mean squares yields the

relationship of the virtual rate constant and the temperature:

ln�̃� = 26,62 ± 2,56 −16600±1800

𝑇 (197)

146

Fig. 57 The Arrhenius line of the examined hydrogen reduction of CuCl.

The Arrhenius-type relationship may also be expressed from Eq. (197) by the proper

rearrangement:

k̃ = 1011,56±1,11 exp (−138000±15000

𝐑𝑇) (198)

It yields an activation energy of 13815 kJ/mol for the hydrogen reduction of CuCl in the

temperature range of 408 – 418 oC. The indicated error margin refers only to the statistical

deviations caused by the experimental errors.

147

Another way of examining the kinetics of the reaction is to record the mass treated material

continuously by applying derivatographic technique. [33Rao, Y.K., El-Rahaiby, S.K., Taylor, W.C.: Trans.

Inst.Min. Metall. 89, 1980, C186.][34Rao, Y.K. ibid. 90, 1981, C47.] In this case, the reduction degree is

derived directly from the change of the sample mass (Δm), and the virtual rate constant can be

expressed as below:

k̃ = {1

𝑚

𝑑𝑚

d𝑡}t=0

(199)

If the sample is heated to the required temperature in a stream of inert gas, the change of mass after

the moment of shifting to hydrogen flow (t = 0) may also serve as a reference.

The activation energy obtained and the type of the process determined can be assessed in

comparison with similar results published. The lower value (~ 138 kJ/mol) obtained above for the

activation energy in the 408 – 418 oC range compared to the 170 kJ/mol value published [33,34] on

the basis of derivatographic measurements in the 300 – 350 oC range may indicate a partly different

reaction mechanism too. The fundamental heterogeneous reaction is dominant at lower

temperatures, whose velocity (Whetero) may be expressed by the following relationship:

𝑊hetero = khetero [𝑝H2/𝑝o −

(𝑝HCl/𝑝o)2

Khetero] (200)

where khetero is the rate constant of the heterogeneous reaction 𝑝H2 and 𝑝HCl are the partial pressures

of hydrogen and hydrogen chloride, respectively, at the surface of the copper chloride and Khetero

is the equilibrium constant. At higher temperatures, the volatilization of CuCl may increasingly

occur, as suggested by V1 curve in Fig. 36.b, which allows the homogeneous reduction of the

evolved vapour of the trimer with hydrogen:

2/3Cu3Cl3,g + H2 = 2Cu,s + HCl (201)

Since the reduction is faster than the volatilization of the salt at these temperatures [33], the produced

copper is deposited in the internal spaces of the pores. It can influence the further process of pore

diffusion and may distort the values of the activation energy determined at higher temperatures

148

because the assumed constant conditions of concentrations and diffusivity may not be valid in this

case and the two different mechanisms of reduction may occur simultaneously. The homogeneous

reaction, increasing in strength at higher temperature, can be considered first order at the high

surplus of the hydrogen supply. Its velocity (Whomo) is expressed as:

𝑊homo = khomo (𝑝Cu3Cl3

𝐑𝑇) (202)

where khomo is the rate constant of the homogeneous reaction and 𝑝Cu3Cl3 is the partial pressure of

the copper mono-chloride gas produced by volatilization. According to the model [34] developed

for the hydrogen reduction of the metal chlorides, the activation energy related to the heterogeneous

mechanism is approximately 180 kJ/mol. The results obtained at lower temperatures are in good

agreement with it. However, the lower activation energy determined at higher temperatures

suggests the increasing role of the homogeneous reaction or the pore diffusion in the mechanism.

The kinetic studies based on the above experiments have demonstrated that the

thermodynamic investigations revealing the feasibility of the chemical metallurgical processes are

not enough in themselves for establishing a devised technology. The methods of metal production

are based on complex processes, whose development into workable technologies requires

investigations of different aspects providing an accurate understanding.

149

Test questions

1) What steps belong to the beneficiation of ores?

a) Crushing

b) Grinding

c) Carbothermic reduction

d) Leaching

e) Flotation

f) Classification

g) Roasting

h) Gas cleaning

i) Cementation

j) Gravity separation

k) Ion exchange

l) Precipitation

2) What methods can be applied for the agglomeration of fine particles?

a) Melting

b) Hydrolysis

c) Pelletizing

d) Casting

e) Sintering

f) Hydrogen reduction

3) What may influence the feasibility of a planned chemical reaction?

a) Particle size

b) Temperature

c) Reagent concentrations

d) Product concentrations

e) Pressure

f) Heat effect

g) Entropy change

h) Heat effect and entropy change together

i) Relative oxygen potential

150

4) How does the standard free enthalpy change of a reaction depend on the temperature?

a) Independent, as the standard state refers to a given temperature

b) It is always dependent

c) It always decreases with increasing temperature.

d) It always increases with increasing temperature.

e) It depends with a linear relationship

f) It is determined by the standard enthalpy change

g) It is determined by the standard entropy change

h) Its dependence varies with the temperature range

i) It is related to the change of the equilibrium constant

j) The same way as the relative oxygen potential

5) What does the electrode potential of metals depend on?

a) Hydrogen ion concentration

b) The pH value

c) Reactivity of the metal

d) The solubility of the metal

e) The concentration of the cations formed

f) Temperature

g) The charge of the metal ions

h) The electric current of the metal

i) Pressure

6) What does the hydrogen overpotential depend on?

a) The cathode metal

b) The type of the dissolved metal ions

c) The concentration of the dissolved metal ions

d) Temperature

e) The pH value

f) The electric current of deposition

g) Exchange current density

151

7) What information is given by the Pourebaix-diagrams?

a) The solubility of metals

b) The possibility of depositing the metal ions at the cathode

c) The formation of metal oxides and hydroxides

d) The effect of pH on the form of the metal in the solution

e) The relationship of the redox potential and the metal ion concentration

f) The phase equilibrium of water

g) The possibility of hydrolysis

8) How is the rate constant of reactions be determined?

a) From thermodynamic databases

b) By mathematical methods from the reaction mechanism

c) By the analysis of kinetic curves

d) From reaction rates measured at two temperatures and constant concentrations

e) From the Arrhenius relationship

f) From the calculated values of the activation energy

g) The recorded changes of concentrations

9) Suitable methods to measure the reaction rates:

a) Execution of the reaction by derivatographic technique

b) Directly measuring the mass change of the starting material

c) Reagent consumption in time

d) Recording the masses of all the products

e) Examining the changing amount of one reagent or product

f) Measuring the heat effect of the reaction

10) What is indicated by a non-linear relationship between the logarithm of the rate constant

and the reciprocal temperature?

a) Exothermic process

b) Measurement error

c) Incorrect expression of the rate constant

d) Multiple step reaction mechanism

e) Changing dominance of key processes in function of temperature

f) Catalytic effect

152

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